I have to agree with Baby Tea, for once.
As far as unrealistic things go, there's nothing special about the 4th movie compared to the original trilogy.
Aliens are still more probable then "working" voodoo dolls, ripping people's hearts out, and I'm not even going to mention a fuckload of working relics artifacts from multiple religions - there were all the Christian things, the obviously-not-Christian magic stones from Asia, and so on.
You really got no ground trying to criticize the new Indiana Jones over it's campiness, (lack of) realism, or even plot. Acting, maybe, but I don't remember it being that much worse then the original trilogy in that department.