We were on the Mariner last month and the parades were the first and last nights. The ice show is not to be missed. I want to say they had it Tuesday and Thurday, twice during those days. You will need to get tickets ahead of time, and there will be long lines. My suggestion is to try and get to the first realease time of tickets, this way you get the show you want. They book up quickly. The show is really great. A lot of the things I read had said that if you didn't get to Johnny Rockets when it first opened you'd deal with lines. We lucked out if we got there around 3:30/4:00. We never had to wait, and were able to get our choice of indoor or outdoor seating. Try and get the waiter from the Phillipines (his name escapes me) - he's great. You can also get take-out and enjoy it in your room or by the pool. We also went at about 12:30 one night,and of course, had notrouble then either. Sometimes it is closed for the Adventure Ocean kids, but this will be listed in your Compass.
I hope this helps. Please feel free to ask any other questions you might have.
We were on the Explorer in January and they announced early on that there would be 2 showings for the early and late dinner seating. They asked ONE member from each family to come to a designated area and pick up tickets for their whole group on the night of their choice. The only bump in the system are those who felt the need to send more than one person so they could get tickets for each of the nights and not have to be committed to one night!! Of course this meant someone else did without but you know there are always though who feel a self elevated sense of importance.
The Ice Show is wonderful and there literally isn't a bad seat in the house. Do remember to bring a sweater though because it is a little chilly especially if you sit near the ice. Have a great time