(As an aside, VLC still crashes on malformed data because the video codecs are written in careless C code. Changing the version number isn't going to fix that bug. )
In general case: for me "version 1.0 not beta" means "we give you the insurance that this software is very stable and reliable. We consider all bugs as important issues. We respect you."
In the case of GMail, I'd like Google to give me this insurance and stop the "no warranty at all, f* you if there is a problem" era. I think they have the power to do it. Would it be really different? No, but I would be able to sleep at night knowing Google takes really care of my email.
True of very few, IME.