While some states do not allow for the remedy of expungement of criminal convictions, Minnesota fortunately does provide for such a remedy. Therefore, you want to go back and petition the court to expunge and seal you misdemeanor conviction. Hopefully, that will solve the existing problem.
You could look into an expungement proceeding, though before doing that I would suggest looking at the whatever government records the problematic background checks are referencing, then go directly to the source of those and see what they say. Sometimes they are mistaken and the mistake can be corrected - more quickly and easily than a potential expungement motion. For example, you may be able to find your case record at the Minnesota courts website http:://mncourts.gov to see if it is accurate, or not. If a misdemeanor criminal charge was dismissed, and the only conviction was for a petty misdemeanor, it should indicate the "level of conviction" is petty misdemeanor (which is not a crime). More at links below.
Please make sure to remember that regardless if you are successful in obtaining an expungement THAT certain professional licenses (Doctor, lawyer, real estate), and/or "law enforcement" positions, and/or "government employment" require YOU to AFFIRMATIVELY and VOLUNTARILY disclose ANY and ALL such matters for "ethical and fiduciary" reasons, whether or not expunged! And failing to disclose the same becomes a separate possible "perjury" issue. Just make SURE you read ANY employment form very carefully as you fill out the same. And, you may be better simply disclosing and explaining the same, as it shows candor and the fact that you have "nothing to hide"....Good Luck!
It depends on what exactly is coming up on your criminal record. Is it the charge or the conviction? There are different standards under Minnesota law for expungement of convictions, (whether based upon a plea or a conviction by judge/jury, or acquittal/dismissal).