I've never had the slightest trouble at check in, and when my wife, daughter, mom, and I go to CZM, we have three coolers. I attached a padlock and hasp to them all, and I used to duct tape them shut, but with the 9/11 security measures, I changed up a little. I use just a clip through the hasp, and I got some web belts and buckles from Academy to replace the tape (I still tape the buckles shut, and I also tape down the pullout handles on the coolers). Sometimes the inspectors open them, but they are no prob to seal back up. I've never had one pop open in transit.
An added advantage is that when we are successful deep sea fishing down there, we freeze dorado (mahi-mahi), tuna, and/or wahoo filets or steaks and bring them back in the coolers. Last year I brought back about 30 lbs of dorado filets, and they were still frozen solid when I got home. Mmmmmm. Fire up the pit!
With the wheels on the coolers and some bungee cords to secure other bags to the tops of the coolers, we can roll all our stuff ourselves through customs and out to the curb in one trip, and I gotta tell you, when I'm traveling with three women on a two week trip to Cozumel, we have a lot of stuff!