Dangers of Driving in Cozumel?

I hear mixed stories about renting a car/Jeep and driving in Cozumel. I know of people who have rented a vehicle and had no problems exploring the island on their own. I've also read on various message boards that you have to be careful of "fake" police who will pull you over and demand cash. Has anyone had either experience? We also heard that it can be dangerous driving in Cozumel as they traffic can be bad (I'm assuming only in the town). We sail on the Mariner of the Seas on June 19th and we plan to rent a Jeep while in Cozumel. Curious to hear of any experiences you may have had.

Mariner of the Seas June,2005
Sovereign of the Seas July, 2003