Not sure how widely known this one is, but I've seen it mentioned on e.g. Wikipedia, so I figured I'd post it.
This paper by Gagola claimed that the commutant of a Moufang loop (the subloop of elements that commute with all other elements) is always normal. This later paper of Griskhov and Zavarnitsine gave a counterexample, of order $3^8$, and mentioned that Gagola had found a hole in his earlier proof.