Tourist Police, as you would guess, assist you in any way possible and ensure your safety and well being. The Municipal Police man stations on the highways near speed bumps to slow and check periodically for contraband, but mostly they are involved in traffic matters.
Federal Police periodically set up road blocks and search for contraband on a random basis. All were non threatening, but did carry heavy weapons and were is strong numbers.
Yes, my wife and I were stopped, and our vehicle searched. The lead officer rummaged in the trunk and a Mexican friend spoke with the soldiers, in Spanish. He offered them cookies and that seemed to break the ice. Somehow, I do not think the cookies could be considered a bribe. As the “Jefe” searched, I stated, in English, that one bag had dirty underwear. He poked it and moved an. Possibly, he chose not to speak English thinking we would chat, and I chose not to speak my broken Spanish. we were soon underway and I was no more upset than if I were run through Airport Security. The more the better!
Then there were the Federal troops. Seen perhaps in the day on a truck or two, but mostly at night. If you went to a beach, or an out of the way park / beach or roamed the woods just in from the main road, you would encounter a band of military, obviously on patrol. They tended to disappear from sight when possible unless they were posted in an area.
Exercise normal care in any City as you would in the States and you should be very safe. Every area has its bad apples. The locals are mostly Mayan, a very nice, soft people. The H1N1 was not apparent either and we were there Easter and the prior week. we return in July and were previously there earlier in the year. Other than the economy, local businessmen are baffled by the large turn down in tourists predicated on problems mostly in other areas of Mexico.... perhaps it is a bargain time to visit Playa del Carmen or Cancun.