Are there any behavioral problems caused by giving your child a cell phone at a young age?

Limit setting. The phone itself (other than cost and media time!) is not the danger. The main issues are setting limits and proper expectations. What is the phone for? Is it used as a 'treat' or a 'prize' for something he/she did... Is it an emergency only tool...A temporary distraction? These are the things to sort out before going down the slippery slope of putting 'hot' gadgets into your child's hands.
Absolutely. All of the doctors comment so far are spot on. Safety is vital, but allowing games, internet, texting etc is unnecessary.This may lead to stranger danger, poor study habits and the like. Thus allowing the phone for location is fine, but web access, use at home should not be allowed.
Cell phone radiation. Debra devra wrote a book called disconnected which is the best thing I have seen out on cell phone radiation and it's dangerous effect on developing beings. Children should only use cell phones in an emergency, optimally with a devise to keep the phone itself away from the body, they should not sleep in the same room as the cell phone and not carry it on their bodies. It is the frog in hot water.
Behavior probs. I published a book on kindle that i think will really help you. It is called: parenting the kids according to a child psychiatrist. It is only $5.95 and i think it will help you a lot, to get your child to behave much better right away. Good luck to you.
Possibly. In today's society keeping track of your child is of paramount importance i i agree. However, it seems to me that "too young" needs to be said. I have a second grader and there are currently no cell phones present. The only 'behavioral' issue i can see is the social reactions from the other classmates; and how your child can cope with them if they should arise.