I did my 1st solo trip (Cozumel/ 1 week/land-based) August 2010, and although I was a bit nervous, it turned out better/smoother than I expected. (did 20 dives, 1 shore dive, 19 off a small boat)
I did do things to try to mitigate 'risk' , as where you're traveling solo it's up to you to deal with 'Murphy's Law' without the help of anyone else.
1) Cozumel is a non-stop flight for me, so less chance of getting screwed by weather, me or my luggage missing a connecting flight or getting separated....keep the air flight logistics as simple as possible.
2) I'd had the hotel/dive arrangements (and the flights too) all set up in advance by a LDS I trust, and that same dive shop has done that exact same trip (same hotel/dive op) many times themselves, so they had scoped everything out personally before hand and knew they wouldn't be sending me on some 'unknown' adventure.
3) as previously mentioned, at least to some extent, you'll pick up (or get adopted by) new friends.
4) I'd even suggest a liveaboard option for you, if you're all about the diving (versus the local tourist scene) you will be surrounded by a high % of hardcore divers (not too many newbies on liveaboards) who will all have a strong love of diving, who on average will be much more experienced than the average land-based diver you'll likely meet, making them better buddies/mentors for you.
5) I agree with the prior observation about having to watch one's bags at the airport while going to the bathroom though...that's one downside to solo travel.