Definitely make sure the O2 is full, test to make sure the reg works, and make sure there's no CO contamination. Might as well analyze it to make sure it's 100% O2 while you're at it.Sure, I'd like to ensure that the boat is safe before boarding, just like I'd like to be sure before boarding a ferry, bus, van, taxi, plane, etc. but there's not much I can check. The one time I requested Oxygen for a diver was at Coz and it failed, but should I start requiring every boat to demonstrate that their O2 kits are onboard and actually work?Why don't you all there take whatever actions that you can to improve safety in that area so as to protect the name of the island.
I am already boarding boats with as much gear as I can carry in one trip, including my own floatation vest I wear while the boat is moving and the DM is strapping my BC to a tank - yeah I'd wear it on your boat too, I'm checking every tank for CO levels for good reason,* carrying all the safety devices on dives I can - far more than most, and I think I'll start checking my tanks for O2 too since I have seen divers on Nitrox who thought they were on air for a deeper dive. I'm doing all I can I think, and hope Cozumel will do their bit.
Test the boat's radio, check to make sure they have sufficient fuel, and do a breathalyzer on the boat driver. Bring a copy of a DM or instructor final exam to test your DM before getting in the water and also have him demonstrate CPR on the boat driver to make sure his skills are up to par. I would also audit the dive operation to make sure they are financially solvent, get a complete background check on the owner, and perform an HIV test on all the crew and other divers on the boat with you in case you might have to engage in mouth-to-mouth and someone has an open sore. Urine testing is also a good idea as you certainly don't want to be on the boat or underwater with drug-crazed loonies.
That's all I can think of for now, but I'm sure there's more you can do.
Oh, yeah, I almost forgot: tinfoil to protect against alien mind-rays that can be intensely focused in the clear waters of Cozumel. Use the good quality Reynolds Wrap broiler foil, not some cheap generic crap. You don't want to trust your brain to cheap foil
