When job hunting, how should I handle problems with references, credit or a criminal background?

Consider waiting for the proper time to address any negative issues with your background (credit history, criminal record, education, references and problems on the job, etc.).
However, address these issues prior to the employer finding out on his or her own. The best approach is to bring these matters up directly acknowledging any wrongdoings, and hope that your honesty, integrity and explanation will override their concerns and turn it into a non-issue.