Realistically, the browser should make no difference at all. But I have seen many strange things happen on different browsers viewing the same page! IE handles Javascript differently, and more slowly than the others, so this can cause it's own issues. Also, IE has it's own set of rules, and until recently (IE 8 beta onwards) didn't really follow the standards like the others do.
But, the "Show New Posts" link should be DataBase driven and not dependant on the browsers. All it needs to do is log the time you were on last, and then search for any new posts since then.
I'll logout now, and come back in IE 8 beta and see what happens...
