I never saw anything wrong with any of the movies' storytelling. It was fantasy after all. I mean a box that holds vengeful spirits which kill everything that looks at them? That was the first film, guys.
Same with me. The first movie had the vengeful spirits, the second had some evil cult, the third had an immortal knight guarding the Holy Grail (and Indy's dad was instantly cured by it). The fridge scene was OK for this sort of a movie and KOTCS was far more enjoyable than The Temple Of Doom.
Besides, as has been said, they're fantasy films. Why does everything have to make sense?