Hmm what I'd do if this ever happened to me. But this is because my room is quite damp as it is and things dont dry over a course of an hour. What I would do is move the frog to another place for the time being. If you have a heat lamp or even a basking light will work(uvb) put it on top of the terrarium. It should dry it up pretty quick. :P If you dont have a heat lamp just take the tank outside and let it sit for 30mins out in the sun. It should dry up alot of it. If the tank ends up being too dry just mist it up again. Also for waterspills.... hmmm.
If your dish isnt too big you could get a plastic bag or a large ziplock bag and put the bottom of the dish on it. Though I use a bowl so this works better for me? In any case do that and get some moss and put it where the dish is. The water will go into the moss. :P