Police officers don’t get elected, but the sheriffs do. I think this is mostly a holdover from when the only real law within a hundred miles of a town was the sheriff.

I do agree that electing judges is odd. My state doesn’t even allow us to vote on electing them anymore, but just on retaining them in office. I’ve always voted “No” just because I don’t think it’s appropriate.

Now if you want to get really weird, most areas also elect their coroner and there usually is no skill or education requirement to be elected.