I've heard stories (from my math professors in college) of grad students who spent multiple years writing about certain entities, which have all sorts of very interesting properties. However, they were having difficulties actually constructing one. Eventually it was demonstrated that there aren't any, and they had been proving the interesting things one could do if one had an element of the empty set.

http://en.wikipedia.org/wiki/Principle_of_explosion

Mathematicians do make errors. Sometimes they brush them aside as trivial (like Girard in Nesov's example), but sometimes they care a lot.