Minnesota does require you to title and register your moped, if you will be using it on city or state roads (use on private property is totally different, of course). If you dont have a title from the prior state, you will have to complete the "no proof of ownership" packet of paperwork and submit that to the bonding committee, where they will decide if its to be bonded or not. Very likely, for a moped, no bonding will be required. When you submit that packet, you will get plates and tabs on the spot, so you can use the 'ped legally on roads. I work for the DMV, and get these questions a lot, so if you need more info, just let me know.
As to whether law enforcement will make problems for you if you dont have it plated properly, that I cant say.
Oh, and if you want that paperwork, to start the process for getting plates and tabs, go to the below link (the state of mn public web page) and click on "contact us" in the bottom left. You can send a request via email there, and just tell them that you need the "no proof of ownership paperwork packet" mailed to you.