I know there were loads of questions about Ryan Leaf's maturity and JaMarcus Russell's work ethic, among other things.
As far as actual legal/criminal issues, I'd have to look back.
The only one that springs immediately to mind is Warren Sapp (failed drug test). You could say Dez Bryant last year, but I don't know that he was a legit #1 candidate.
Lets look at this year. Peterson seems to have recruting issues as well and yet I don't see many folks other than you saying that it changes their mind about picking him for example. There are still folks saying pick him despite the fact that his past is shady and he scored the lowest wonderlic of any top prospect right next to Green's very low score as well.
If you look back at Vince Young, sure the comment was made was made that his mother was a prostitute but did anyone really trash him because his father was in and out of prison most of his life and he admitted being a gang member as a youth. The fact is he was in fights and conflicts in high school.
There were numerous incidents a the end of college where he:
Colt Brennan wasn't the top pick but he has legal issues and spent time in jail while in junior college before going to Hawaii.
It was the intangibles, however, that concerned many. When the Longhorns were invited to the White House to receive congratulations from President Bush, Vince showed up in jeans and a sweatshirt, while his teammates came in suit and tie. He skipped an important meeting with Reebok and blew off commissioner Paul Tagliabue’s party at the Super Bowl. He also scored low on the Wonderlic Test, which measures a player’s ability to absorb NFL playbooks. Rumors circulated that Vince had a scored a six out of 50, which the test administrators said was untrue. His actual score was never reported.
But one night in January 2004, Brennan’s world went spinning. After a night of drinking, he was accused of sexual assault, indecent exposure, burglary and criminal trespass by a female neighbor.
In September of that year, a jury found him guilty of unlawful sexual contact, but a judge dismissed the charge three months later. Still, Brennan was found guilty of second-degree burglary and first-degree criminal trespass for not leaving the woman’s room in a timely manner.
He was sentenced to seven days in jail, one night of which he spent with a cellmate charged with attempted murder. He also completed 60 hours of community service, picking up trash, and is currently serving four years’ probation.
I don't remember a huge outcry when he was drafted.
And the list goes on.