What can I do if a past employer gives false information about my employment?

Essentially, you have three options. The first is to do nothing. But if this has truly harmed you, then there are two other options. You can explain to the former employer that this behavior is unacceptable and they need to rectify their behavior. Unfortunately this route is fraught with tension. An employer may take that as a cue to cover up the prior behavior. The final option is to retain an attorney to sue the employer for various torts including but not limited to defamation. There may be other business torts depending upon the specifics of the situation that may be helpful as well.