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.
Continuity mistake: Mutt's bike passes by a group of strikers in the campus, and heads for the red banner. When the angle changes, a second group of strikers has suddenly appeared out of nowhere next to the banner.
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 Mutt and Indy run away on the bike, there's a shiny red car parked behind. A mere frame later, a dusty greyish car has magically appeared parked next to it.
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: In the race between the soldiers and the youngsters in the roadsters, there is a shot of boots on the military vehicle's pedals and the next shot is of sneakers on the same pedals.
Continuity mistake: At the start, after Irina Spalko unsuccessfully reads Indy's mind she slaps him a few times. Then she lowers her hand, but in the following close-up the hand is raised and being lowered again.
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: During the ants scene, Indy is about to grab a stick to the left of his hat. In the close-up the stick and the hat have swapped sides.
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.
Continuity mistake: When the Akator temple starts to move, the sand by the groups' feet keeps changing from sandy with a couple of rocks, to filled with weeds and leaves, and back to sandy.
Continuity mistake: In the alien room, Spalko walks to Ox to take the skull away from him. In the first angle Marion is standing to the left of Ox, but in the immediate close-up she is behind him.
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.