Continuity mistake: When the group enters the final temple the skull falls into the water. Mutt picks it up, and there's a shot of Mac grabbing some gold. Then back to a wide angle and Mac is repeating the previous movement with a totally different hairstyle.
Revealing mistake: At the end Indy picks up a heavy slab and uses it to knock the carved faces off the wall. He hands it to his friend Mac, then takes it back off him - at this point it's clearly a very light prop.
Continuity mistake: In the wedding scene the bride has open toed shoes when she kisses Indy and begins to exit the pulpit area, but different closed toe shoes as she and Indy depart the church.
Continuity mistake: After Mutt points at the waterfall, Indy grabs the skull and Mutt leans on him to raise up, yet a frame later from a different angle his hands are away from Indy.
Continuity mistake: When the raft is about to fall through the second waterfall, there's a huge rock to the left which disappears in the wide angle.
Continuity mistake: When Indy removes Orellana's golden mask, the light changes abruptly from very shiny to obscure and mysterious.
Continuity mistake: During the quicksand scene, when Mutt is throwing a snake at Indy, Indy's left (our right) sleeve swaps from covered in sand to spotless between shots.
Continuity mistake: When Mutt and Indy enter the library, a chubby man in a suit holding a brown briefcase runs away, yet appears calmly walking half a second later from a different angle.
Continuity mistake: During the ant scene, the branch that Indy uses to knock out the Russian wasn't there in the first place, it magically appears between shots.
Continuity mistake: After Mutt's bike knocks down the "Better red than dead" banner it falls sideways; yet when the chasing car arrives, the banner is magically up again, ready to fall horizontally on the car's windshield.
Audio problem: During the chase inside the campus, a car destroys some stone vases and a blonde woman cries in terror while running away, yet her mouth is not moving.
Continuity mistake: When Indy and Mutt's bike is about to exit the campus, a green car is passing by, which disappears in the immediate wide angle of the street.
Continuity mistake: When Mutt and Indy ride inside the arched door in the campus, a couple runs away, yet appears still there from the opposite angle.
Continuity mistake: When Indy and Mutt are about to enter the university, the guard is holding both gate doors almost closed. A frame later he's holding one completely opened.
Continuity mistake: When Indy is about to hop on Mutt's bike, a man walks behind him twice. First time slowly, second time fast.
Continuity mistake: At the Mexican market, while Mtt is playing with his pocket knife, watch the chrome part of the light: it reflects a barren place with a brown squared building. When the angle changes it all changes to a bus and a lot of people hanging around.
Continuity mistake: Inside the waterfall, Ox takes out the skull, moves his hand from the top to the side of the skull. The angle changes and the hand remains on the side, but when the angle changes to behind Ox his hand is on top of the skull, repeating the first movements.
Continuity mistake: Inside the waterfall Ox takes out the skull while Marion watches from behind. When the angle changes, her hand is suddenly on his shoulder.
Continuity mistake: Indy uses a huge rock to smash the stone where sand is coming out and hands the rock to Mac. From one shot, Mac falls backwards and sits down, but from a different angle he is standing up slightly crouched.
Continuity mistake: Ox takes out the skull, Marion walks behind him, moving to a corner on the right. In the next angle Indy says, "Ox, I think I understand" and Marion is suddenly gone, only to magically reappear a frame later.
Answer: People felt it was ridiculous and cartoonish, even by Indiana Jones standards. Even if it was possible to survive a nuclear blast via the lead lining of a fridge (it's not), or that the fridge would simply be thrown away rather than be melted/torn apart like everything else in the vicinity (it wouldn't), the impact of being flung what appears to be a mile or so through the air, then violently crashing into and rolling over the ground, would certainly kill anything inside. The controversy arose because usually, in "classic" Indy films, the fantastical elements were exactly that: fantastic, magical, and/or supernatural. This was presented as taking place in our reality, with no "power of God" or magic spells, and for many, that was just too much disbelief to suspend.