Can someone please tell me of a way to find out if potential employers are getting bad information about me without my knowing?
You have to create some fake HR departments who will pretend to be interested in hiring you. Have them call your references and former employers.
Get friends and relatives to make the calls, using your scripts, while you listen in. You can't make the calls yourself because someone would recognize your voice.
There are some good suggestions in the links DarkCygnus provided. If you find you're being ruled out of job applications at the reference stage (usually after you've accepted the job offer), you could certainly ask the prospective employer - but they may not tell you.
If you're being ruled out before the job offer stage, a more likely explanation is that another candidate looked like a better fit. I've been on both sides of this, and while it's easy to wonder about what you might have done "wrong", in most cases it's just that someone else was chosen. (Though I'll agree that leaving the other candidates hanging is plain rude.)
There are also some other suggestions which genuinely surprise me. Trying to fool people is never a good approach - if you don't already have a bad reputation, that's one way to get one.