Bar regulations (like exams) vary from state to state, so do your preemptive homework before selecting a school. Misdameanors are not serious crimes and do drop from a criminal record after sucessfully completing probation and letting time pass (~seven to ten years). By that time you will be graduating anyway.
You do make a valid point about felonies though. Felonies come in every shade of every color, and some states do consider DUIs/DWIs felonies. Others even classify defaulted child support to be a felony punishable by imprisonment. Depending on the state, I know it is possible (but extremely difficult) to be admitted into the bar with a felony conviction. Still, I have read of individuals with serious criminal records that managed to "turn their life around" and practice law even after serving time. It's rare, but not impossible.
As far as I know, most (even elite) b-schools don't conduct a thorough investigation of all their MBA candidates. If they did, I know a few people who managed to slip through the cracks.