I've heard things across the entire spectrum from yes absolutely, to no not at all. My guess is some where in between, but more towards having a fairly large impact. More and more medical schools are doing background checks, and that will likely become universal in the coming years.
I know that some schools do judge a candidates judgement during the interview process, so a DUI at 18 can probably be explained away easier than one at 22 as youthful indescrestion. And underage drinking is probably not as bad as DUI.
When I was interviewing at KU, there had been a terrible ice storm the day before, and the school had - in advance of the storm earlier in the week - sent out an e-mail telling the students who were scheduled for that day to not worry about coming in if the weather was bad, that they would reschedule with no penalty, etc...Well many of the people e-mailed back saying "I'll be there" and stuff like that. The Dean of Admissions was like "well do I mark you as having poor judgement or not if you are telling me that you'll be here no matter what despite awful dangerous weather". She was saying this in jest, but underscored an important point.