If you do not like second hand smoke, do not go on the Explorer of the Seas. Smoking is permitted on one side of the ship and in the Casino. The Royal Promenade is open to the Casino one deck below. The smoke permeates the Royal Promenade and is distasteful for non-smokers.
Otherwise, the ship is quite nice but not necessarily any better than Carnival, Holland America or Princess.
Ice show was awesome. and the other shows in the Palace Theatre were mixed. Singers and comedians were good. However, not enough variety.