Status bars aren't really designed for error messages. If you can't use dialogs then I would either use in line error messages using a simple JLabel. You can set the font so that it is red, etc. If you don't have room per say for in line error messages, then create a message header on your form of some sort that can display error messages above all the components. Really, it's not that different than displaying error messages in web pages, if you are familiar with that at all.
Take a look at the
JGoodies Validation Demo. It will give you some good ideas. You may even want to use that package.