The papers were published in the May 1995 issue of Annals of Mathematics. Thousands of people have a read them. About a hundred understand it very well. Faltings has simplified the argument already. Diamond has generalized it.
People can read it.
The immensely complicated geometry has mostly been replaced by simpler algebra. The proof is now generally accepted. There was a gap in this second proof as well, but it has been filled since October 1994. This synopsis is quite brief. A full survey would run too many pages.