How liable am I for my user's uploaded content? I understand that there is a DMCA law for this that says that as long as I comply to demands for removal of copyrighted content, then I can't be sued for my users files. True? Not True?
You won't have any trouble as long as you delete it when you are asked to. Are you hosting files or just text? If it was files, I'd check periodically for illegal material just to be safe. If it was text, don't sweat it.
That's true provided you have a clear method of flagging infringing content, remove it within a reasonable time, and that you remove content you know is infringing (movies etc.) - even if you aren't notified of that infringement.