Grunwald's Theorem on the existence of extensions satisfying local data was well known and widely used; Whaples even gave a second proof of this result before Wang found a counterexample and closed the gap. A similar mistake occurred when Shafarevich proved that solvable groups are Galois groups over the rationals - the case of 2-groups was "problematic".

On a more fundamental level, Kummer's proofs of unique factorization into prime ideal numbers had gaps because he did not know about the concept of integral closure. This gap was noticed and closed only by Dedekind.