Like I don't mean "this proof has a gap in its justification, but the thing claimed likely is still true". I mean "we thought someone had a proof for X, but actually later someone else showed X isn't true".
The short version is that Gödel claimed in a paper that he had an algorithm to determine satisfiability for a certain logic, but the algorithm actually worked for a slightly different logic instead. People basically took Gödel's word for it for fifty years until a logician called Goldfarb found the mistake.
EDIT: As a disclaimer, I don't have any association with or endorsement of the website I've linked to. I found it just now because I needed a source for the story that I've known for many years (I think I first heard it in person, but it's definitely contained in the book `The Classical Decision Problem' by Börger, Grädel and Gurevich). I skimmed the post and it seemed to cover the relevant details, but that's the extent of my knowledge of the site and its contents.
OTOH, there was the Italian school of algebraic geometry, but that was more than one single flaw...
[0] https://mathoverflow.net/questions/35468/widely-accepted-mat...