Firstly: 

The science of hadeeth and isnaads (chains of narrators) is one of the special characteristics of this ummah. No other nation paid attention as this ummah did to the chains of narration through which their books and their religion were transmitted. This is why the texts of other nations were subjected to distortions and fabrications, and it became impossible for them to know the pure religion and to find out about the stories of the Prophets in a sound and authenticated manner. 

The scholars of hadeeth have striven hard and reached a prominent position in that field, as Allaah has honoured them with efforts to preserve His religion and the Sunnah of His Prophet (peace and blessings of Allaah be upon him). 

Muhammad ibn Haatim ibn al-Muzaffar (may Allaah have mercy on him) said: Allaah has honoured this ummah and favoured it over others by blessing it with the isnaad. No other nation has this blessing, and they do not distinguish between that which was revealed in the Tawrah and Injeel and was brought by their Prophets, and that which was added to their books of narrations transmitted from inauthentic sources. This ummah narrates hadeeth from a trustworthy individual who was known at his own time for sincerity and honesty, from another of similar character, and so on until the end of the chain of narrators. Then they researched very carefully to find out who had the stronger memory and was more precise, and who spent more time with the one from whom the report was transmitted, and who spent less time, then they would write down the hadeeth from more than twenty chains of narration, so that they could be sure that they had eliminated any mistake or error from it, and they wrote it exactly as it was narrated. This is one of the greatest blessings that Allaah has bestowed upon this ummah. We ask Allaah to inspire us to thank Him for this blessing and we ask Him to make us steadfast and to guide us to that which will bring us closer to Him and make us adhere to obedience to Him. End quote. Sharaf Ashaab al-Hadeeth (40). 

Secondly: 

They are the best people who strove the most to ensure that their judgement and transmission of hadeeth was done on the basis of honesty and sincerity, and they were the ones who strove the most to avoid errors and mistakes, to the extent that they set the highest example of fairness and avoiding favouritism when it comes to preserving the religion of Allaah.  

So we see ‘Ali ibn al-Madeeni ruling that his father was da’eef (weak), and he knew that this ruling regarding his father would guarantee an end to his position as a scholar, but that did not prevent him from stating his opinion concerning him. 

Al-Khateeb al-Baghdaadi (may Allaah have mercy on him) said: 

None of the people of hadeeth should show any favouritism with regard to the science of hadeeth, whether it is to his father or his son. ‘Ali ibn ‘Abd-Allaah al-Madeeni, who was a prominent scholar of hadeeth in his time, never narrated even a letter to suggest that his father was strong in hadeeth, rather what was narrated from him was the opposite of that. End quote from Sharaf Ashaab al-Hadeeth (41). 

Ibn Hibbaan said in al-Majrooheen (2/15): 

‘Ali ibn al-Madeeni was asked about his father and he said: Ask someone else. They said: We asked you. He paused, then he raised his head and said: This has to do with religion; my father is da’eef (weak). End quote. 

And Yahya ibn Ma’een spoke about a friend of his whom he loved, and al-Husayn ibn Hibbaan narrated that he said of Muhammad ibn Saleem al-Qaadi: By Allaah, he is our friend, and he is dear to us, but there is no way to praise him and I do not recommend anyone to narrate from him or encourage others to do so. And he said: By Allaah, he heard a great deal and he is well known, but he does not limit himself to what he heard, rather he includes things that he did not hear. I said to him: Should he be narrated from? He said: No. See: Tareekh Baghdaad (5/325). 

Jareer ibn ‘Abd al-Hameed said concerning his brother Anas: He should not be narrated from; he tells lies when he talks to people. Al-Jarh wa’l-Ta’deel (2/289). 

Imam al-Bukhaari narrated a great deal in his Saheeh from his Shaykh, Muhammad ibn Yahya al-Dhuhali, in spite of the harm that he was subjected to as a result of a misunderstanding between him and the Shaykh, who forsook him. But that enmity did not prevent him from accepting and narrating his hadeeth. 

They would accept hadeeth from those who held different opinions and beliefs to their own – if it was proven that (the narrator) was honest and sincere. The fact that a narrator was a follower of bid’ah did not prevent them from judging him on the basis of fairness, because they paid heed to the words of Allaah (interpretation of the meaning): “O you who believe! Stand out firmly for Allaah as just witnesses; and let not the enmity and hatred of others make you avoid justice. Be just: that is nearer to piety; and fear Allaah. Verily, Allaah is Well‑Acquainted with what you do” [al-Maa’idah 5:8]. 

Yahya ibn Ma’een was asked about Sa’eed ibn Khuthaym and he said: He is a Kufi and there is nothing wrong with him; he is trustworthy. It was said to Yahya: Is he Shi’i? He said: A trustworthy Shi’i, a trustworthy Qadari. Tahdheeb al-Kamaal (10/414). 

‘Abbaad ibn Ya’qoob al-Rawaajini al-Kufi was a fanatical Shi’i, but despite that, Ibn Khuzaymah said in his Saheeh (2/376): The one who is trustworthy in his narration but dubious in his religious commitment, ‘Abbaad ibn Ya’qoob, told us … 

Thirdly: 

Just as they understood the seriousness of tarnishing people’s honour unlawfully, they also understood the seriousness of speaking badly about any of the narrators, because it could affect the issue of accepting or rejecting the hadeeth of the Messenger of Allaah (peace and blessings of Allaah be upon him) from them. Muhammad ibn Sireen said: This knowledge is the (foundation of) religion, so watch from whom you learn your religion. Narrated by Muslim in the Introduction to his Saheeh. 

Ibn Daqeeq al-Eid said: 

The honour of the Muslims is a pit of Hellfire. Two groups are standing at the edge of this pit: the muhadditheen and the judges. End quote. See: Tadreeb al-Raawi (2/369). 

Such great piety and awareness must inevitably have a great effect of fairness and seeking to be right when judging narrators. This is what was stipulated by the scholars for everyone who wants to examine narrators and pass judgement concerning them. 

Al-Dhahabi said in al-Mooqizah (82): 

Judging narrators requires a great deal of piety and freedom from whims and desires and bias, along with complete experience in the science of hadeeth and the faults and narrators thereof. End quote. 

Al-Mu’allimi (may Allaah have mercy on him) said in al-Tankeel (1/54): 

The imams of hadeeth are knowledgeable and careful, and they strive to avoid mistakes, but they differ with regard to that. End quote. 

Fourthly: 

Yes, none of them is infallible and it is possible that there may be mistakes in what some of them say. It is also possible that the cause of some of these mistakes may be love or hate for someone. Some things of that nature did indeed happen, for no human being can be entirely free of that. But that should not be a reason for doubting all of their judgements, and this is for the following reasons: 

1 – Because these are a few mistakes when compared with the great legacy that the leading scholars of hadeeth and al-jarh wa’l-ta’deel have left behind, the vast majority of which is based on honesty and fairness, so it is unfair to overlook that because of a few mistakes. 

2 – Because the scholars highlighted these mistakes and pointed them out in their comments. Whatever the motive was, whether it was enmity, envy or a difference of madhhab, they would reject unfair judgements and would issue fair judgements concerning a specific narrator. 

Hence none of the scholars accepted the view of Imam Maalik concerning Muhammad ibn Ishaaq, the author of al-Maghaazi, that he was one of the fabricators, when they realized that this statement was based on resentment and personal reasons; rather they judged him as “hasan al-hadeeth” (i.e., a good narrator) and the leading scholars of hadeeth used his reports as evidence. And they did not accept the view of al-Nasaa’i concerning Ahmad ibn Saalih al-Masri, or the view of Rabee’ah concerning Abu’l-Zinnaad ‘Abd-Allaah ibn Dhakwaan. See: al-Raf’ wa’l-Takmeel (409-432). 

Abu Haatim al-Raazi (may Allaah have mercy on him) said: There has never been in any nation since Allaah created Adam safekeepers who preserve the legacy of the Messengers, except in this ummah. A man said to him: O Abu Haatim, perhaps there were narrations which have no basis and are not sound? He said: Their scholars will recognize the sound from the unsound. So they preserved this science (of hadeeth) so that the people who came after them were able to distinguish between reports and preserve them. Then he said: May Allaah have mercy on Abu Zur’ah; by Allaah he strove very hard to preserve the legacy of the Messenger of Allaah (peace and blessings of Allaah be upon him). Sharaf Ashaab al-Hadeeth (43). 

You should understand that Allaah has preserved this religion by His grace and blessing, and that the Sunnah has been preserved as Allaah guaranteed to preserve His religion. [See the answer to question no. 77423.] So it is not possible for the scholars to unanimously agree to authenticate a weak narrator or to criticize or condemn a sound narrator. Rather you will inevitably find that truthfulness and fairness are very apparent in the views of the majority of scholars and in most issues of religion. 

Imam al-Dhahabi (may Allaah have mercy on him) said in al-Mooqizah (84): 

The same imam may be more generous or more kind with regard to a report that is in accordance with his madhhab or the madhhab of his Shaykh than with regard to other reports that say the opposite. But it is only the Prophets who are infallible.  

But this religion is supported and protected by Allaah, may He be exalted, and its scholars will never agree on misguidance, either deliberately or by mistake. So no two scholars will agree on classing a weak narrator as sound, or on classing a sound narrator as weak; rather their differences will be with regard to how strong or weak a narrator is. The one who passes such judgements speaks on the basis of his own effort, strength and knowledge. If it so happens that he makes a mistake in judging, then he will have a single reward. And Allaah is the source of strength. End quote. 

Ibn Katheer said in al-Baa’ith al-Hatheeth (1/11): 

As for the words of these imams who took on this task (of examining hadeeth), they should be accepted without questioning or mentioning the reason, because of their knowledge of it and their deep understanding of this field, and because of their being known to be fair, religiously committed, experienced and sincere, especially if they agree unanimously that a narrator is weak, or matrook (to be ignored) or a liar and so on. The skilled muhaddith will not hesitate to agree with them when they take a decision of that nature because of their honesty, trustworthiness and sincerity. Hence al-Shaafa’i said in many instances when commenting on ahaadeeth: “None of the scholars would regard this hadeeth as sound,” so he would reject it and not quote it as evidence on that basis. End quote. 

With regard to what you referred to about the words of Shaykh al-Mawdoodi – may Allaah forgive him – in the book of his that you mentioned: even though Shaykh al-Mawdoodi was one of the pioneers of da’wah in the Indian subcontinent, and he confronted many deviant ideas and made great efforts in da’wah and writing, nevertheless, like any other human being, he was not infallible and free from error, especially when he spoke about things that he was not qualified to discuss and that were not his specialty, as is the case with the matter referred to in the question. The Shaykh (may Allaah have mercy on him) made many mistakes with regard to his views on the Sunnah and the method of the scholars of hadeeth with regard to judging and distinguishing between ahaadeeth. We do not have enough space here to mention them and refer to them. Many specialized scholars have pointed this out, including the great Pakistani scholar Muhammad Ismaa’eel al-Salafi (may Allaah have mercy on him) who died in 1387 AH. He wrote an important study entitled Mawqif al-Jamaa’at al-Islamiyyah min al-Hadeeth al-Nabawi (attitude of the Jama’at-e-Islami towards the Prophet’s hadeeth). See also – in Arabic – Zawaabi’ fi Wajh al-Sunnah by Salaah al-Deen Maqbool Ahmad (p. 117 ff). 

Finally, you should be content with the blessing that Allaah has bestowed upon this ummah by means of this noble branch of knowledge, and do not get carried away with doubts about the saheeh ahaadeeth. Reason dictates that we should not reject the efforts of thousands of sincere scholars throughout the centuries on the basis of a few mistakes here and there. I think that what you have on your mind is no more than whispers from the shaytaan, so seek refuge with Allaah from them, and do not pay any attention to them.  Strive to read books about the science of hadeeth, and I am sure that you will be astonished by the huge efforts that were made to authenticate a single hadeeth. This is what is believed by everyone who studies the books of hadeeth and the sciences of hadeeth and biographies of narrators. Even the Orientalist Margoliouth said: The Muslims may boast about their science of hadeeth. 

And Allaah knows best.