The Criticism:
In the movie, our hero and his companions wind up facing worshipers of a goddess called Kali (kind of like in "Help!"). As they attempt to escape, members of the Thuggee cult attempt to takeover the mind of Indiana Jones (Harrison Ford) - and steal his heart - literally. Some viewers find the portrayal of this historical group offensive, as there were apparently actually religious zealots worshiping Kali and killing up to a million in her name. Furthermore, India briefly banned the movie on grounds of cultural insensitivity.
Critics also dislike Willie (Kate Capshaw), Indy's love interest in this film. Used to finer things, Willie's not the world's best companion when it comes to adventuring with elephants and creepy crawlies. (She also screams a lot.)
Lastly, some viewers are offended by Short Round (Jonathan Ke Quan), Indy's underage Asian sidekick. This kid drives cars and it's clear Indiana's a mentor to him, but critics call out the immoral treatment of the child because in real life, Indiana would be putting him in danger.