You did a great job summarizing the cruise. I will add a few things that we did differently than you.
Shows: We saw most of the shows - enjoyed the comedian, magician, and Hughes Bros group. Did not enjoy the Rhapsody singers/dancers as much. We missed one singer (Kenny James) that we heard was good.
Dinners - agree with you, most things were good. We had lots of flexibiltiy in ordering mixture of appetizers, soups, whatever. Waiter brought DH and primerib and lobster on 2nd formal night. I don't like lobster so he brought me a plate of shrimp along with my prime rib (the shrimp was shared around the table - way too much for me). We mostly ate in Windjammer for lunch/breakfast. We tried dining room for breakfast and lunch the last sea day. The breakfast was ok, would stick with WIndJammer for that. Lunch however was nice with different food selections than WindJammer. Wished we would have had lunch in there a few more times.
We enjoyed the games, laying out at the pool (love the Mango Tangos!). I went to gym in the a.m twice and used equipment - not a lot of room but you can make it work. I liked walking on the outside deck also.
Grand Caymen was too crowded. We took taxi to Sea Grape Beach and luckily we were somewhat early because it got crowded. We had a nice time though.
Cozumel - we were on same Eagle Ray excursion (3 reef with lunch). Lunch was not that great and I thought we were going to have time to relax on the beach but all we did was eat lunch and then load back up. Maybe they were worried about getting us back to ship on time. My DH said we had the slowest boat out there which made the trip longer than it needed to be. Also, the 3rd reef was not near as good as the first 2 so you made the right choice in just doing the first 2.
All in all it was a great cruise with great people and weather! I would recommend this ship also and it seems to be less expensive than any of the ones in Florida. If you don't need a Voyager class then this is the way to go.
One note - we did not have a mini-frig in our room which surprised me. Cabin steward said only the upper decks have them on this ship. We did have a safe though.
Next Cruise: ALASKA - 2016
Explorer of the Seas - Jan 2015, Liberty of the Seas - Feb 2014, Oasis - May 2013, Freedom of the Seas - Jan 2013, Navigator of the Seas - Dec 2010
Liberty of the Seas - Sep 2008, Jewel of the Seas - Feb 2008, Sovereign of the Seas - July 2005, Rhapsody of the Seas - Feb 2005