A nice example of a mistake that caused a big setback to its field when discovered, and led to a big upsurge when it was finally fixed, was Dehn's lemma in 3-manifold topology.
Dehn used the lemma in 1910, believing he had proved it, and for a long time it was thought to have established a simple connection between knots and the fundamental group.
In 1929, Helmuth Kneser discovered a mistake in Dehn's proof, which wrecked his plan to write a book on 3-manifolds based on Dehn's lemma, and probably caused him to change fields fo several complex variables.
The field of 3-manifolds did not become very active again until Papakyriakopoulos finally proved Dehn's lemma in 1957.
