One quick tip... be sure to note your time zones and set your watches accordingly, especially if you are getting on and off the ship!
We saw an older man run almost the entire length of the pier in Cozumel because he did not do this. He boarded after the whistle sounded for the last passenger aboard and almost missed the ship. Everyone who happened to see him running from their balconies (like us) was cheering him on and telling the crew to wait. I'm sure he'll never do that again.
Even though there is no internet service (unless you bought one of the plans), be sure to set your phone/iPad, etc. to whatever time zone you are in if you take it off the ship. I had mine still set on "set automatically" for New York, Eastern Daylight Time. I got off the ship in Grand Cayman which is an hour earlier and unknowingly, came into a wifi area. My iPhone which I had set one hour ahead, reverted to its original NY time setting and I thought I had missed my tour! Thankfully, I had not, but to avoid any unnecessary panicking...