Yes, yes, and yes. No, no, and no. Just depends on who you ask.
In 2009, he was arrested at 3:47am for public intoxication as a 20yr old. Some people will say the starting QB at an SEC school should lead by example, others (myself included) will say "and your point is, he's in college."
Some question his accuracy on simple, short throws. He's admitted that he needs to develop more touch on passes underneath because defenses have keyed on taking the vertical passing game away from him. Some will say this reminds them of JP Losman who could throw it a mile, but not hit a guy on a simple slant pass. Others will say this is something good coaching can easily correct.
For a good laugh, check out his mug shot though. Funny stuff.