I really subscribe to the attitude in this post. We're developers, we're supposed to make decent software. Our users won't care whether it's our fault or somebody else's if the software doesn't work. Just like you don't go blaming the database if your app becomes slow, you shouldn't blame the browser for rendering your page wrong, even if you're right!
Dammit, we're grown ups here. Make decent software! Test it! Automate the tests! Gracefully degrade! Yes, it's difficult, yes, it's costly! Get over it already!
Either make a fancy web app that works, or just make it highly non-fancy (HN, anyone?) to avoid all the headache. Or go somewhere halfway, as long as you're in control.