Thawing in hot water from the tap is by far the safest way to go. The speed of bacterial growth is a temperature x time equation, and the quick nature of hot-water thawing ensures an absolute minimum of bacterial growth before feeding because of the limited time spent at the higher temperature.
Conversely, placing a mouse (or rat) in the fridge or on the bench for 12-24 hours will allow far more bacterial activity to take place before feeding. Our food animals are intact with all the gut contents, there are huge amounts of bacteria living in the gut of all animals, most are harmless, but even a slight rise in temperature for a few hours will accelerate the growth of harmful bacteria unacceptably.
Mice will usually thaw in about 5-8 minutes, larger rats may take a couple of changes over a 20-30 minute period, and just check that the animal feel fully thawed by pressing your fingers into its belly to ensure it is warmed through.
I usually feed wet if I'm not using fresh-killed, and as others have indicated, I believe it helps with hydration. I have never had a problem feeding wet, and my snakes are just as enthusiastic about a wet meal as a dry one.
Jamie.