It's using millisecond precision time for the nonce, yes. Nonce collisions in a normal volume chat are unlikely. If you'd like to suggest improved counter code, however, I'm all ears. :)

A corrupted server could alter messages without the key if it had both the plain and encrypted versions of a text. But to get that, the javascript would have to be compromise, and at that point the server might as well just steal the key anyway. This has already been discussed above, and if you're worried about it, the solution is actually pretty trivial. I especially like Whimsy's suggestion of a Grease Monkey script for verification.