Revealing mistake: After Indy escapes from the conveyor belt, he runs on some suspended planks while being shot at. Watch the planks: There's black masking tape where the explosives are (which disappear in later shots). Furthermore, right before he takes out his whip, he grabs a railing where the bullet has just hit, and you can see that the black tape is dangling loose after the spark.
Revealing mistake: During the mine chase, after Indy cries to Shorty "Let it go, our only chance!" the wig of the doll replacing Willie flies away. (01:35:59)
Continuity mistake: During the palace dinner scene, the "snake surprise" is laid down at Willie's left side. A few shots later it's on her right.
Continuity mistake: After Short Round breaks the Maharaja's spell, the blood on the side of his mouth swaps from a thick strand to a thin one between shots.
Revealing mistake: When Indy is put inside a cage Short Round comes to hug him. There's a shot of Indy from behind and he is a noticeable stand-in: Thinner face, clean hair, no sweat, and clean shaven instead of stubble.
Answer: He says "kali ma, shakti day". This is hindi and means (literally) "black mother, give me power/strength". "Ohm nama Shivaya" means "I bow to Shiva." Both are Hindi.