Canada

they deal with more types of case than they should.

I could see them functioning as a sort of 'first line' point of contact with the justice system for crimes without a victim other than 'the state', and that don't result in potential jail time or massive fines. Jaywalking, littering, speeding, noise violations, etc. There's no reason an actual judge should be tied up with the simplest of cases that won't have much in the way of evidence one way or another. Someone with the statutes available and common sense should be all that's needed for that sort of thing.

Allow them to decide to dismiss cases, but allow for appeals to a real judge if people who are judged guilty demand it, with the ability of that real judge to declare the appeal frivolous and impose extra court costs if the appeal fails.

Sort of an entry 'tech support' for the court system.