In my reading of mathematics I often run into propositions that are stated without proof. If I can I write out the proof for myself. I have these proofs scattered over notebooks, which is not very convenient.
I think it would be great if math.SE had a special "sub stack" where people could post their proofs of propositions, with a reference to the original source of the proposition (a book, a paper, etc.). One could choose to make one's proof public, so that others can vote on it, and offer feedback (maybe point out missteps or gaps, or ways to improve it).
I'm thinking of something similar to github's gist, but for math rather than source code. From what I can tell, the site already has all the necessary "plumbing" to make the implementation of this additional feature relatively easy.
Of course, the same format should allow the posting not only of proofs, but also of other mathematical items, such as definitions, counterexamples, and constructions.
Over time, this could grow into a great repository of mathematical "brass tacks".