How many links in a press release is too much?

Um no - no matter what your excuse, 50 links in a press release would always be inappropriate. I have to assume from that post that you have no idea what press releases actually are other than perhaps thinking of them as glorified articles.

And Jimbob - There's nothing wrong with a link in the first paragraph. In fact, I'd consider it incredibly irresponsible not to have a link (URL written out in most cases) in either the summary or first body paragraph, or both - especially if the primary thing being publicized is a website or online business. The moment someone forgets that releases are for readers and not search engines is the moment they sabotage their SEO efforts with them in the process.