We are still having issues with browsers compatibility. We are also working on that.
I just (when writing this answer) fixed compatibility with Firefox 3.6 and Opera ;)
So it seems to work on Firefox 3.6, 4, Chromium, Opera (on Linux platform at least). However it may not work for everybody :/
It's not expected to work on IE8.
We recommand
Firefox 4 (beta) for now ;) Others may also work.
If you still have issues try to force-refresh the whole website ;)
Therefor, close osu-web tab, wipe browser cache, go back to osu-web, try shif+F5
Edit : doesn't work on Opera for now