Deciding what version of a result to cite is always tricky business. Often the original sources are obscure and much better versions of that result exist in survey articles or textbooks. Recently, I've reviewed two papers which have cited the Nerve theorem, one crediting Borsuk and another Leray. Here's the first question:
Who was the first to prove the Nerve Theorem?
The authors of one of these papers had cited Bjorner's generalization of the Nerve theorem. It is clear that they had not read Bjorner's work because it very clearly requires paracompactness of the underlying topological space; two paragraphs before "using" the theorem, these authors had proved that their space was not paracompact! So, I have the following second question:
Let's say that you have cited a result from some paper or textbook. What is the probability that you have carefully read through the relevant section or chapter?
I don't intend to be flippant or rude, but it seems very unlikely that everyone reads through everything that they have cited. Rather, if one wants to use a theorem that is not in a standard textbook, one typically finds another paper which cites the desired result and steals that citation, thereby passing the responsibility of ensuring correctness to someone else. This saves a lot of time, but seems to propagate inaccurate citations and poor understanding of the work being cited.