I've noticed this for some time, but have yet to find a fix or see a post from someone else with this same problem. I use Firefox nearly exclusively, and my blog posts appear in that browser formatted exactly as I wrote them from the menus in WP, i.e. bold, italics. I occasionally write about TV shows and books, and thus need to set those titles off in my writing.
However, in viewing these same posts in Safari and Chrome, all of that formatting is gone. Just regular 'roman' type. So frustrating!
I'm sort of a grammar stickler, so I'd hate for readers using other browsers to think I'd neglected to follow some pretty major rules.