Your question is...how do you know when fish go bad? Or does slime mean they are bad?
Not exactly sure what you are asking.
Most scaly fish produce that slime when they are put on ice or in really cold water. The slime has nothing to do with whether the meat is still good.
If the fish are cold, they should be fine. Not cleaning the fish might affect the flavor a bit after a day or two (meat being "marinated" in the cooler), but they will be ok for a while. I have thrown ice on fish that I didn't have time to clean for a couple of days with no ill effects.
When you are cleaning them, take the back side of your knife blade and rake it across them to get rid of some of the slime, and it will reduce the amount that gets all over everything. I also recommend getting some gloves of some sort (I have some mesh ones with rubberized grips) to help keep you from freezing the ends of your fingers off.
As a free general tip - hand sanitizer works really well at getting the fishy smell off your hands. I generally wash my hands with soap and water, then follow with hand sanitizer, and 90+% of the smell is gone in one shot.
