I'm very particular about my feet/footwear while at Disney, so no flip flops for me. They don't provide enough comfort or support for all that walking. It's only my Nike New Balance shoes all the way while there. I usually bring two pairs just in case they get soaked through. If you know it's going to rain (or if it's summer) I tend to pack a fresh pair of socks with me when I go to the park.
The following are always with me at the parks (some are shoe related):
-poncho
-bandaids (for blisters)
-sunblock
-sunglasses
-camera, extra memory card, extra charged batteries
-fresh pair of socks
-water bottle and crystal light packets
-key to the kingdom
-credit card
The rain is great. Sometimes I wear my poncho. If it's really muggy, and the poncho is going to be uncomfy, I just keep it off and get soaked. I don't really care, frankly. The feet, though, yeah. I will change into dry socks as soon as I am able and the rain has stopped.