Some of my users are reporting that longer messages in chat seem to be getting cut off? Is there a character limit I don't know about? I couldn't find anything like that in the options.

Yes, our MySQL database is configured to only allow 500 characters at a time.

Could there be some indication of this on the user side? I mean, I'm sometimes typing away thinking it's all gonna fit. I have no way of knowing unless I count each character.

Not a bad idea. Javascript counters can be a solution, although there are technical issues to address first (an apostrophe will actually be 5 characters for instance).