Can I get a passport with a bench warrant?

My boyfriend has a non-extradition warrant in Minnesota. He got a DUI some time back, went to jail for about a month and was released on probation. He moved then, to Hawaii, without really thinking about the need to inform anyone. When it came up, he went home to deal with the paperwork and the lady in charge was supposed to file it all and he returned thinking everything was hunky-dorey. He recently got a job at a bank and they informed him that his background check brought up a bench warrant in MN.

My first question is, if it was a pure mistake, is he likely to have to do more time in jail in order to clear this up? And my main concern is that we are supposed to be going on a trip to Europe this summer. Can he get a passport with a local bench warrant, and if not- will they try to arrest him for attempting to get one?

Any insight would be great! Thanks
KM

Local bench warrants will often not show up nor prevent passport applications...but it is best for him to resolve that asap.