A timeline of his legal issues:
April, 2014 - Forced his way into a girls apartment after she tried to close the door on him. Girl fell down some stairs. Beckham alleges he was looking for his girlfriend. Girlfriend pressures the girl who fell down the stairs not to press charges.
No arrests made, Beckham voluntarily enters counseling. Dismissed from Mizzou.
January, 2014 - Arrested on suspicion of felony drug possession, where the car he was riding in was found to have roughly a pound of marijuana. Beckham fully cooperated, and was the only one of three to provide a DNA sample and cell phone records without a warrant.
Pretty sure this got thrown out as nothing. Still suspended from Mizzou.
2012 (freshman season) - Arrested for marijuana possession
Each of these incidents doesn't appear (to me, anyway) to be that much to be concerned with long-term. Together they form a pattern, which is definitely somewhat concerning.
But overall you have to trust the guy in the room to evaluate his character, evaluate what he's been doing for these last 15 months and make a judgement call from there.
At this point I still trust Farmer to do that.