Different bugs in different browsers, certainly. Firefox for example suffers from known serious bugs that nobody fixes for years, because nobody happens to feel like it and the bug only affects a small number of sites anyway. Which is fine so long as you don't want to use one of those sites.
There's so much broken stuff out there on the web (eg sites deliberately engineered not to work on a particular browser, people still basing sites on Ext
JS 2.2 that works up to IE 8 but not on IE 9, etc etc) that you might well find that you need more than one browser these days.