* The antagonists. While the evil russians looked cool and we finally got a break from nazis, the main villain, this chick with mental powers, is beyond lame. Not only she never uses these abilities (only once at the beginning, yet she fails miserably) and we never get any form of explanation of what they're supposed to be or where they came from, but she also barely manages to beat Mutt in a swordfight. Like, she should've owned him in seconds. Maybe I missed something about her powers because I had to get up a couple of times, but still, it never really pays off. Not to mention, they got into the warehouse with all the artifacts from history, and they never even check any of the boxes? And shouldn't that place be heavily guarded anyways?
* Individual scenes that just stretch our suspension of desbelief to its limits. I know these kind of movies aren't made to be taken seriously, but are we really led to believe that you can use a huge snake as a rope, or get in a refrigerator to survive an atom bomb? It's like they're trying to be as absurd as possible just to test us, it almost feels like a cartoon. The fridge scene I actually had to explain it to myself by saying that Indy has a more enduring body because he drank from the Holy Grail in the last movie, so he basically has near immortality (his dad still died so I guess he will too eventually, but not from wounds).
Its been a while since I've seen this. (Come to think of it, its been a while since I've seen any of the Indiana Jones movies). So some of what I'm think might be out of date, or me miss remembering things.
With the Russians mental powers-I got the impression that she didn't really have any. Like it was a bluff to get people to talk. Or she thought she did-but it was a self delusion.
As for the fridge, people have pointed out Indy survived equally absurd situations before. Like stopping a mine car with his feet. Hiding in a sub's tube, which would have been filled with water-thus drowning him.
I agree with some of the other stuff you said.