Some basic information
First of all you should be aware that none of the hadith scholars and authors of hadith collections compiled in their books all of the hadith they have memorized through out the time they were studying and learning.
Imam Malik as was reported had compiled his al-Muwatta' from a source of 100.000 narrations: al-Muwatta however has -depending on the riwaya- somewhere between 530 and 720 ahadith + other narrations and commentaries so that it contains at most -and by adding all different riwayaat- less than 5000 narration. It is said that when teaching al-Muwatta' imam Malik started with around 10.000 and with the time reduced this amount, by filtering weaker narratives.
As for the imams al-Bukhari and Ahmad it was reported that they had memorized 600.000 (some say less but the amount certainly is above 300.000) narration while imam al-Bukhari only compiled about 3000 of them in his Sahih while he mentioned many more in other books, imam Ahmad -who didn't intend to only compile sahih hadith- compiled around 40.000 hadith.
What do I want to say with this: When a hadith scholar chooses a hadith with a certain chain then because he came to the conclusion that this is the most trustworthy and most sane chain, by comparing both hadith content (al-Matn المتن, literally: the text, body or back) and hadith narrator chain (as-Sanad المتن, literally: the pillar, voucher, support or deed). This is a complicated and stingy investigation which I'll try to explain rather superficially -if I found examples I might add them later or simply refer to them-.
Be aware that most of the hadith scholars used to spend a lot of time with their teachers, so that they got a good impression about them. Nevertheless both are human and one may notice some human attributes in their works etc.: They are not infallible. Therefore the investigation doesn't end if one found a single statement of an earlier scholar. For example imam al-Bukhari consulted some of his teachers for a long period of time, but when it comes to compiling their hadith you may find him compiling only a few narrations or not even one in his Sahih, but some more in other books.
Further if a hadith scholar compiled a statement of a person adding the narrator chain it is up to the reader to verify it's correctness, as the author only transmitted what he has noted or heard and compiled it blunt. This is why most (if not all) original hadith compilations and also books that were compiled on the topic of 'Uloom al-Hadith usually contain a narration with the full chain. In many cases these books were addressing experts not laymen.
Books that were meant for laymen are rathher "easy readings" books like Riaydh as-Saleheen (hadith) of imam an-Nawawi or Siyar 'A'laam an-Nubala' سير أعلام النبلاء (history/biography including a qualification of narrators, mainly only biographys of well identified/known people are quoted in this book) of imam a-Dhababi etc. where the full narrator chain is mostly not mentioned and the focus is rather on the content or the information shared than on the qualification of this content and its reporter. However one must notice that none of them excludes a small quantity of da'if narrations or narrators who report some statements. But usually the author avoids sharing information that is regarded as doubtful or haram etc.: the information is useful and free from bid'ah or anything that may cause harm (in the faith and worship practices) to the person reading it.
An example to explain the methodology
Let's try to explain it:
A hadith Scholar has at hands a hadith report with different chains: Students (A, B, C) -> Scholar X -> Tabi'iy -> Sahabi (reported from the prophet).
Let's assume that the hadith scholar already qualified the level of trust for the Tabi'iy and the person I've called "Scholar X", by comparing narratives with mainly the same content of the hadith as it was reported by the Tabi'iy and found out that "Scholar X" used similar wordings as most or let's say better the majority of his mates and the content of his reports is not questionable neither from accordance to qur'an, other reports that were qualified as sahih and has no linguistic issues if all of this apply he would come to the conclusion that "Scholar X" is trustworthy.
Now he might start checking the students let's say that Student A was the first to study hadith from his teacher and he began his studies around the year 160 a.H. (all this needs to be checked by the hadith scholar) and he remained studying for at least 2 or 3 years, let's say that Student B started his studies in the year 162 a.H. (the hadith scholar may check whether he met A etc. too) and he was impressed from this teacher and decided to follow him for at least one decade while Student C only met his teacher more than 10 or more years later. Now if the reports of our hadith report from the Students A, B and C matches one could conclude that our Scholar X had a good memory (at least until the time Student C consulted him), if there was mismatch between the Students A and B (and C) one may check the memorization abilities of the students if only Student C's report mismatches the other reports one may come to the conclusion that our Scholar became a bad memory in later ages.
This is just a simple example and each conclusion must be checked and re-checked by comparison between reports of the same content and light deviations in the chain.
Additionally a scholar may also consult conclusions from earlier scholars if he trusted them.
Statements about the methodology
An early statement can be found in Sahih Muslim:
علامة المُنكَر في حديث المُحَدِّث: إذا ما عُرِضَتْ روايتُه للحديث على رواية غيره من أهل الحفظ والرضا، خالفتْ روايتُه روايتَهم، أو لم تكد توافقها، فإذا كان الأغلب من حديثه كذلك، كان مهجورَ الحديث، غير مقبوله، ولا مستعمله
An indication of Munkar in the narration of a Muhaddith is when his transmission differs with the transmission of a Muhaddith from the people of memorization and acceptance, or does not agree with it when the two are compared. When the majority of a person’s narrations are like that, he is abandoned [Mahjūr] in Ḥadīth, and not accepted in it, and his narrations are not acted upon.
فمن هذا الضرب من المحدثين عبد اللَّه بن محرر ويحيى بن أبي أنيسة والجراح بن المنهال أبو العطوف وعباد بن كثير وحسين بن عبد اللَّه بن ضميرة وعمر بن صهبان ومن نحا نحوهم في رواية المنكر من الحديث. فلسنا نعرج على حديثهم ولا نتشاغل به.
The following are those Muhaddithīn who are among this group: Abd Allah ibn Muharrar, Yahyā bin Abī Unaysah, Al-Jarrāh bin ul-Minhāl Abūl-Atūf, Abbād bin Kathīr, Husayn bin Abd Illah ibn Ḍumayrah, Umar bin Suhbān, and those of the same type in terms of transmission of Munkar Ḥadīth. We did not pause upon their narrations or preoccupy ourselves with them due to the ruling of Ahl ul-Ilm.
(Source the introduction of Sahih Muslim)
اعلم أنَّ أكثَرَ المُتَكَلَّمِ فيهم، ما ضَعَّفَهُم الحُفَّاظُ إلا لمخالفتهم للأَثْبَات
Know that the most talked about them (criticized), where not declared as weak by the hufadh, but for their contradiction to more reliable.
(A-Dhahabi in his al-Muqidah المُوْقِظَةُ -see below 19- المضطرب والمُعَلَّل-)
About abu Hanifa in Jarh wa-Ta'adil
Mainly abu Hanifa is not regarded as a the best source of hadith, some (trustworthy) scholars reported about him being unaware of certain sunnah acts, others had issues with the fact that he rejected ahaad hadith, this mainly was the same issue some scholars had with imam Malik, however what speaks for Malik is his good memory and he lived long enough to teach people and had a high sanad.
Another point that is often quoted is abu Hanifa's definition of iman: it is constant and can't grow or change which is the majority view and scholars concluded that he made a difference between uttering and acting in the matter of faith (iman). It is said that al-Bukhari only quoted from people who held the majority view in his Sahih (needs to be verified). Scholars considered fiqh scholars who hold this definition as murji' in fiqh which is different from murjiah.
Among the best hadith scholars abu Hanifa consulted were Hammad ibn Sulayman and 'Ata' ibn abi Rabah (if he really met him as some reports doubt it) among others.
Also note that scholars of Jarh and Ta'adeel might not have left out any hadith scholar from a kind of criticism, this is not because they want to defame a person, but rather due to the importance of sanity of reports from the perspective of statements like: This knowledge/science is a religion (see Did Imam Malik describe the hadith sciences as "this science is a religion"?).
In his "short biography of abu Hanifa" imam a-Dhahabi quoted some favorable statements from certain scholars, I've added in brackets an overall qualification about them based on what I could find in Siyar 'alaam an-Nubala' itself and elsewhere:
قال محمد بن سعد العوفي : سمعت يحيى بن معين يقول : كان أبو حنيفة ثقة لا يحدث بالحديث إلا بما يحفظه ، ولا يحدث بما لا يحفظ .
Muhammad ibn Sa'ad al-U'awfi said (he is considered as da'if and a narrator of rejected hadith) said: I've heard Yahya ibn Ma'iyn saying: Abu Hanifa was trustworthy thiqah narrator that did not narrate hadith except with what he memorizes, and does not narrate what he does not memorize.
وقال صالح بن محمد : سمعت يحيى بن معين يقول : كان أبو حنيفة ثقة في الحديث ،
Salih ibn Muhammad from Baghdad (trustworthy and student of ibn Ma'iyn) said: I've heard Yahya ibn Ma'iyn: abu Hanifa was trustworthy thiqah in hadith.
وروى أحمد بن محمد بن القاسم بن محرز ، عن ابن معين : كان أبو حنيفة لا بأس به . وقال مرة : هو عندنا من أهل الصدق ، ولم يتهم بالكذب .
And Ahamd ibn Muhammad ibn al-Qassim ibn Muhriz (narrator of the Tareekh -history- of ibn Ma'yn and rather unknown narrator!) reported from ibn Ma'yn: Abu Hanifa was nothing wrong laa ba'sa bihi (in hadith). He once said: He is among the people of truth, and he has not been accused of lying.
(Imam a-Dhahbi Siyar 'alam an-Nubala')
In his book on Jarh wa Ta'adeel Mizan al-'Itidaal ميزان الاعتدال a-Dhahabi wrote a rather objective short (which sounds unfavorable) note -as is the case in books on Jarh wa Ta'adeel-:
9092 - النعمان بن ثابت بن زوطى، أبو حنيفة الكوفي.
An-NU'maan ibn Thabit ibn Zoota, abu Hanifa from al-Kufa.
إمام أهل الرأى.
The leader of the people of Ra'y.
ضعفه النسائي من جهة حفظه، وابن عدي، وآخرون.
An-Nassa'y declared him as da'if from the perspective of his memorization, and so did ibn 'Ady and others.
وترجم له الخطيب في فصلين من تاريخه، واستوفى كلام الفريقين معدليه ومضعفيه.
Al-Khateeb (al-Baghdadi) dedicated him a bioghraphy in two chapters in his history, and cited all statements of both sides those who consider him trustworthy and those who consider him weak.
He also mentioned in Diawan al-Du'afaa'wa-l-Matrookeen ديوان الضعفاء والمتروكين:
النعمان: الإمام رحمه الله، قال ابن عدي: عامة ما يرويه غلط وتصحيف وزيادات، وله أحاديث صالحة، وقال النسائي: ليس بالقوي في الحديث، كثير الغلط على قلة روايته، وقال ابن معين: لا يكتب حديثه.
An-Nu'maan may Allah have mercy on him. Ibn 'Aday said: What he narrates is generally wrong, corrections and increases, but he has sane hadiths. Al-Nasaa’i said: He is not strong in the hadith, he has many errors compared to his low amount of narrations. And ibn Ma'yn said: his hadith shouldn't be written down.
On the other hand except with a handful exceptions and narratives imam abu Hanifa's hadith was not quoted in any of the six books.
A contemporary scholar has discussed and compiled all statements of Jarah and Ta'adeel about abu Hanifa and add and verified the qualification of those who reported or made such a qualification in a book called: نشر الصحيفة في ذكر الصحيح من أقوال أئمة الجرح والتعديل في أبي حنيفة where he quoted 77 authors of statements positive and negative. Most of these reports come to the conclusion that abu Hanifa is ranged somewhere between sadooq and da'if al-Hadith, which means he mainly has no high quality (linguistic errors, maybe paraphrasing reports: incorrectness of the statement etc.) nor high sanad or at least he had some flaws in the hadith he memorized, many scholars spoke about his memorization and erroneous quotation of hadith.
Just to clarify tiqah, mutqin, tabth are describing the highest level of trust and memorization and excellence: the hadith of such a person can be written with high confidence. sadooq or laa ba'sa bihi is the second one or at least a lower level trust. Anything below is rather a negative. But be aware that scholars may have different definitions or classification a standardization only started with the efforts of ibn Salah.
See also: Is there a scale or classification for scholars and their qualification of hadith narrators?
Further sources used in this post -Arabic sources-:
- Fatwa wa abu Hanifa from Murji'ah islamweb #106466.
- Notes about abu Hanifa in Al-Bukhari kitab a-Dua'fa' as-Saghir كتاب الضعفاء الصغير and at-Tareekh al-Kabir التاريخ الكبير.
- Why didn't al-Bukhari narrate via a-Shafi'i and abu Hanifa? Fatwa islamqa #221368.
- An article on islamweb about the level of saddoq in al-Jarh wa Ta'adeel.
- An investigation on ibn Muhriz.
- An article on Jarh wa Ta'adeel.