Here's my advice, and it's coming directly from personal experience: Do nothing.
I was that kid. I was there. I was slamming down books like The Phantom Toolbooth in my first grade year, I was better at math than anyone else, and I was pretty well-adjusted. The teacher had myself and another student enlisted in a support role as an aide during the afternoons, and things went pretty well, in general.
But then, my mother decided that I wasn't being challenged enough, so she took matters into my own hands, and decided to skip me ahead a year. All of a sudden, I was a year younger than everyone else - developmentally and socially - and it made a pretty big difference. My classmates were always bigger and faster at me at playground games, and I was almost always picked last. I was a year behind socially, too - they were all into sports, while I was still bringing stuffed animals to school. They realized that I was an easy target, and I got ridiculed constantly; they resented me because I could keep up with them in the work, even though I was younger than they were - "You're not supposed to be in this grade!" was the worst. After that year, I got put in the same classes as most of those kids for years after (let's hear it for being in a small town!), and I never really lived it down. As a result of having very few friends, I spent most of my highschool career glued to a computer screen, rather than going out and doing whatever fun things that higschool kids get to do. It took me a few years (and a very patient girlfriend, who is now my fiancee) to properly bring me into the 'real world' and to teach me how to properly interact with people.
Now, I understand that my situation is a bit extreme (and I'm definitely not trying to show off my sob story!), and there were some other factors at play (bad parenting, for one), but the fact is that children develop really really fast at that age - to the point where depriving them from just a year's worth of social development could have some really detrimental effects.
It sounds to me like you've got a pretty bright kid, and that he's probably headed for college after high school. Remember that if you put your son ahead a year, then you'll probably be shipping him off to college a year earlier than otherwise.
Also remember that if he sails through elementary and middle school, that it's very likely that he'll still be pretty enthusiastic about school in general when he hits high school, and that he'll have the chance to be in AP classes and get some college credit while he's there. Making it through elementary any faster really won't do much for him, in my opinion.
So, with that being said, I'd encourage you just to encourage him to do his best, and to leave him where he is and let him develop at the same pace as his peers. If he breezes through the work in first grade, then he'll probably breeze through it just as much in second or third grade, if you were to put him ahead - by and large, the work isn't that much more difficult - so I'd have to say that the behavior issues you've mentioned would be something completely separate. If he doesn't feel 'challenged', maybe you could see if there are some after-school activities he could be part of. Maybe send him over to Stack Overflow and let us turn him into a programmer. :D