First of all i have to correct some information in your question.
The full name of sahih al-Bukhari and its meaning
al-Bukhari was born in Bukhara which nowadays isn't located in Iran but in Uzbekistan and neither of those two countries existed or had those names at the time AFAIK. So saying he's Iranian is like some Arabs pretending ibn Sina to be an Arab or ibn Ajurum to be an Arab instead of saying his a Muslim or a Persian Muslim. Let's say his a Persian Muslim!
The full name of Sahih al Bukhari is الجامع المسند الصحيح المختصر من أُمور al-Jami' ul-musnadu as-sahihu al-mukhtassar min omori rassuli Allahi salla Allahu 'alayhi wa salam wa sunatihi wa ayyamih رسول الله صلى الله عليه وسلّم وسننه وأيامه!
The name itself explains a lot: This book is collection of the sunan and the days (biography and history of what happens during the lifetime) of our Messenger (peace be upon him) but it was also qualified as a collection which supported (by narration chain) and also summarized.
Now if we found a narration in sahih al-Bukhari without sanad then this could mean that it is not sahih unless we find in another chapter the same narration with a sanad! as The book also includes also some narrations which fall under the name "athar" as it was the habit at the time.
Therefore only ahadith have been checked by contemporary scholars (among them Ahmad ibn Hanbal, Yahya ibn Ma'yn and ibn al-Madyni) who said they found the whole book sahih except for 4 ahadith, but al-'Oqayli added the statement of al-Bukhari is the right one: They are all sahih/sane (According to ibn Hajar al 'Asqalani in "tahdhib at-Tahdhib تهذيب التهذيب" ج9 ص54)!
Jamal al-Bana and his book
Jamal al-Bana or Gamal al-Bana wasn't a scholar but one could say an author and a Muslim thinker or better less a scholar than a liberal Muslim thinker! He was the younger brother of Hassan al-Bana the founder of the Muslim Brotherhood!
In his book he didn't say that all these 635 hadiths (or narrations) are fabricated or incorrect. But he said that they don't have any meaning/use or are not binding for Muslims: This means they don't affect anything in their live, for example who cares about what the Messenger (peace be upon him) used to wear (which colors) etc. as long as there is no clear order to do the same.
Of course he pointed out a couple of ahadith which he considered to be incorrect. As they present a bad picture of Islam and our Messenger in person (Peace be upon him)!
He also pointed out a couple of ahadith the 4 Imams of sunni schools knew but refused, as they contradicted to better known ahadith or in cases to the Quran! So some of his statements were not new but well known!
Note that except for the 8-10 ahadith which are rejected by one of the 4 Imams for some reasons al-Bana din't even try to discuss any of the other 6XX hadiths in any plausible way. All he did was quoting them according to a topic or classification. So these ahdadith are rather among those who are not binding for Muslims or are useless for our life as Muslims.
So the new in al-Bana's book is that he see that this book isn't 100% binding for Muslims which differs from the statement in the fatwa of islamqa!
Is Sahih al Bukhari 100% authentic?
Ibn Hajar al 'Asqalani did some criticism about some narrators in about 110 ahadiths (32 of them are also in Sahih Muslim) he himself qualified them to be weak etc. but he also said as they were teachers of imam al-Bukhari he knows them best and he said that the weaknesses in those ahadith are not of the kind one have to reject them (to be found in al-Kholi's book Miftah as-Sunna which gives a great overview about the hadith sciences and their early history)!
Sheikh Mohammad al-Ghazaly did like Jamal al-Bana some criticism about the matn of some ahadith in his book السنة النبوية بين أهل الفقه وأهل الحديث as-Suna an-Nabawiya bayna ahl al-fiqh wa ahl al hadith (Sunna between the faqihs and the hadith scholars). And they are not the only ones!
Some criticized ahadith (Maybe some are not in Sahih al-Bukhari):
- the Prophet Musa (peace be upon him) hitting malak al-mawt and knocked out his eye.
- The age in which our Messenger (peace be upon him) married 'Aisha (May Allah be pleased with her)!
- that the Messenger (peace be upon him) added by fault something to the Quran when talking to Quraish.
- statements about the virility of the Messenger (peace be upon him).
- some statements about woman.
- some statements which present our Messenger (peace be upon him) as a bloodthirsty person.
And here's the website of a scholar or a student with ahadith from both sahih books which he claims are da'if!
From this we see that no hadith collection could be free from criticism and this is fully ok! As we have only to believe that the Quran is free and safe of mistakes etc.
Sunni people and scholars say that the both Sahih books of al-Bukhari and (then) Muslim are authentic this means that the number of ahadith which might be incorrect or doubtful over them is marginal maybe less then 1-2%. But still nowadays some scholar check and review them and this goes along with the sunni thought that nobody is infallible except the Messengers (Peace be upon them).
Therefore it's right to say "There is no book beneath the canopy of heaven that is more sound than al-Bukhari and Muslim, after the Qur’aan." as said by ibn Taymiyah or "...The book of Bukhari is the more authentic of the two and more useful" as said by ibn Salah. However earlier Scholars from al-Andalus used to set sahih Muslim higher then sahih al-Bukhari (the reasons for that would be interesting to check!)!
On Nu'aym ibn Hammad نعيم بن حماد
Nu'aym ibn Hammad ibn Mo'awiyah ibn al-Harith ibn Humam ibn Salamah ibn Malik al-Khoza'i al-Marozi (abu 'Abdillah) نعيم بن حماد بن معاوية بن الحارث ابن همام بن سلمة بن مالك الخزاعي، المروزي (أبو عبد الله) was a teacher of imam al-Bukhari and he was a great scholar of fiqh and faraa'id (inheritance matters) and author of many books, but his hadith narrations have a bad taste as a-Dhahabi said in his Siyar a'alaam an-Nubala' سير أعلام النبلاء (see here in Arabic) we he quoted a couple of hadith narrations which were rejected by many scholars which Nu'aym ibn Hammad al-Marozi narrated and spread. Imam al-Bukhari has only quoted a hadith of his teacher once in his Sahih in the book of "Merits of al-Ansaa"r on the authority of 'Amr ibn Maimun (see here) who only described what he 'Amr ibn Maimun (not the prophet()) witnessed in Jahilya. So the authenticity and correctness of this narration doesn't really matter as it is strictly speaking not a hadith. Nevertheless al-Bukhari used to quote some of Nu'ayms narrations in his other books where he didn't explicitly say he would rely only on sound narrations with full narrator chains. Imam Muslim actually quoted Nu'aym ibn Hammad only in his introduction when he listed statements and quotes on "Unveiling Defects of the Transmitters of Ḥadīth and Relaters of Reports and the Statements of the A’immah Regarding That" (see here). This again is not a hadith nor even comes close to that.
Al-Bukhari under (political) pressure?
I would like to add that some modern scholars tend to say that al-Bukhari was also pressurized from some authorities because of a story which could be find in many books which introduce the hadith sciences (for example in fath al-bari of ibn Hajar al-'Asqalani), where Muslim (the author of the sahih) asks him about a Hadith about "atonement for what takes place in the assembly" and al-Bukhari apparently didn't want to tell the hadith with the chain Muslim was indicating, which apparently was stronger than the one al-Bukhari cited at first,so al-Bukhari told him: "hide what Allah has hidden, ..." this chain included al-Hajaj ibn Yusuf the known tyrant of the Omayyad dynasty (whom narrated it from ibn Jurayj), so the reason for the political pressure here is that people who are loyal to the Abbasids might denounce him for quoting a symbol of the Omayyads as a reliable source!
قَالَ – أي البخاري - اسْتُرْ مَا ستر الله، هَذَا حَدِيث جليل رُوِيَ عَن الْحجَّاج عَن ابْن جريح.
but Muslim was insisting until al-Bukhari dictated the Hadith. Muslim at the end said: "Only an envier could hate you, and i testify that there's nobody like you in this world (dunya)!
لَا يبغضك إِلَّا حَاسِد، وَأشْهد أَن لَيْسَ فِي الدُّنْيَا مثلك
Note that among of the witnesses of this conversation are many well known Hadith scholars like Imam at-Tirmdihi, an-Nasa-i and ibn Khozaymah.
As an addition you can also read the details of the fatwa from islamqa quoted by @Abdullah.
Well as a Muslim i'd like to say sahih al-Bukhari and sahih Muslim are the most authentic books of sunna but i think as they are human they could include some mistakes or fabrication.
And i ask myself why the earlier scholars like Imam Abu Hanifa and Malik toke ahaad ahadith with big care and rejected them if they had "better" proofs according to their osol. While later Scholars like Imam Ahmad and a-Shafi'i accepted them and gave them a higher value in Jurisprudence while everybody knew that with the time hadith fabrication was more and more diffused!
And Allah knows best!