Theoretically this topic is covered to some extent in the fatwa islamqa #122507. I'll try to give some examples -without quoting nor discussing the narrator chains, note that all these examples are in at least one of the two sahihs and the qualification of the content has no consensus-:
EXAMPLE 1: Marriage while in the state of Ihram is prohibited
An example of this is the hadith of ibn 'Abbas:
Narrated Ibn `Abbas:
The Prophet (ﷺ) married Maimuna while he was in the state of lhram but he consummated that marriage after finishing that state. Maimuna died at Saraf (i.e. a place near Mecca). (Sahih al-Bukhari, sahih Muslim, and in the sunan books and Jami' at Tirmidhi)
Which is in clear opposition to the narration on the authority of Yazid ibn al-Assam:
Maimuna daughter of al-Harith narrated to me that Allah's Messenger (ﷺ) married her and he was not in the state of Ihram. And she (Maimuna) was my mother's sister and that of Ibn 'Abbas (Allah be pleased with them). (Sahih Muslim, also reported by at-Trimidhi
And also narrated on the authority of abu Rafi':
"The Messenger of Allah married Maimunah while he was Halal (*), and he stayed with her while he was Halal, and I was the messenger between the two of them." (Jami' at-Trimidhi)
(*) Halal in this context means "not in the state of Ihram", while Haram means "in the state of Ihram".
Sa'id ibn al-Mussayib clearly says that ibn 'Abbas has misunderstood:
Sa’id bin Al Musayyib said There is a misunderstanding on the part of Ibn ‘Abbas about the marriage (of the Prophet) with Maimunah while he was in the sacred state. (Sunan abi Dawod)
Beside this there's a more general hadith:
I heard 'Uthman b. 'Affan say that Allah's Messenger (ﷺ) had stated: A Muhrim must neither marry himself, nor arrange the marriage of another one, nor should he make the proposal of marriage.
(Sahih Muslim -with several narrations-, similiar narrations are also in the sunan and al-Muwatt'a and Jami' at-Trimdihi)
And many other narrations prophibitting the marriage while in state of Ihram such as in Jami' at-Trimdihi and a verdict of 'Omar ibn al-Khattab al-Muwatt'a. (This is also covered in islamqa #159220, so far only available in Indonesian and Arabic).
Note that it could simply be that ibn 'Abbas was too young and didn't witness this marriage.
EXAMPLE 2: When an addition is shadh
An addition in sahih Muslim is strongly disagreed by imam Malik:
The Messenger of Allah (ﷺ) said: The purification of the utensil belonging to any one of you, after it is licked by a dog, lies in washing it seven times, using sand for the first time.
(For details see Airport dogs checking our bags, Are Dogs Impure? and finally What kinds of sin does hadith rejection lead to (if any)? -which includes ahadith rejected by the four Sunni Imams)
EXAMPLE 3: The hadith about the basmalah
We have on one side the sahih hadith on the authority of Anas ibn Malik saying:
The Prophet, Abu Bakr and `Umar used to start the prayer with "Al hamdu li l-lahi Rabbi l-'alamin (All praise is but to Allah, Lord of the Worlds). (Sahih al-Bukhari and sunan abi Dawood)
And a narration on the authority of Anas ibn Malik saying they started with the Basmalah: "Bismi Allahi ar-Rahmani ar-Rahim...":
I observed prayer along with the Messenger of Allah (ﷺ) and with Abu Bakr, Umar and Uthman (may Allah be pleased with all of them), but I never heard any one of them reciting Bismillah-ir-Rahman-ir-Rahim loudly. (Sahih Muslim, also in sunan an-Nasa-i, sunan ibn Majah and Jami' at-Trimidhi who commented it saying that practice is not to say it loudly).
This hadith is in opposition to narrations of more trustworthy narrators!
Imam an-Nasa-i also complied a hadith on the authority of Abudllah ibn Mughhaffal showing that reciting al-Basmallah aloud was not regarded as permissible.
Let's leave the two sahihs for now: A big source of ahadith which have a -or an apparently- sound narrator chain is al-Mustadrak of imam al-Hakim. Before insulting this great imam I should point at the fact that al-Hakim himself already pointed at some kind of shadh ahadith in his book which are narrated by rather trustworthy narrators (those narrator chains which are present in both sahihs). (Also read Is al Hakims Hadith collection Al Mustadrak reliable?)
EXAMPLE 4: 7 Earths and in each a Prophet like yours
On the authority of ibn 'Abbas (this is strictly speaking not a hadith):
) الله الذي خلق سبع سماوات ومن الأرض مثلهن ) قال : سبع أرضين في كل أرض نبي كنبيكم وآدم كآدم ، ونوح كنوح ، وإبراهيم كإبراهيم ، وعيسى كعيسى . (source)
My own translation:
On Verse "It is Allah who has created seven heavens and of the earth, the like of them. (65:12)" He said: seven Earths and in each one of them a Prophet like yours, and an Adam like Adam, one Nuh like Nuh, an Ibrahim like Ibrahim and one 'Isa like 'Isa.
Al-Bayhaqi quoted this hadith on the authority of his teacher al-Hakim in his book al-Asma' wa as-Sifaat and added:
قال البيهقي : " إِسْنَادُ هَذَا عَنِ ابْنِ عَبَّاسٍ رَضِيَ اللَّهُ عَنْهُمَا صَحِيحٌ، وَهُوَ شَاذُّ بِمُرَّةَ ، لَا أَعْلَمُ لِأَبِي الضُّحَى عَلَيْهِ مُتَابِعًا ، وَاللَّهُ أَعْلَمُ " (source islamqa #229594)
(My own translation take it carefully):
The reference of this chain to ibn 'Abbas may Allah be pleased with him is sahih (correct), and it is clearly irregular (shadh) I don't know of any other continuation except the one of Abu Doha (the narrator who heard it from ibn 'Abbas) and Allah knows best!
Imam a-Dhahabi seems to confirm this in his talkhees (see in Arabic islamqa #229594). Also note that ibn abi Hatim has a similar quote in his tafssir.