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: Inside the waterfall temple, the group walks by a room (with a passage on each side and a double entrance with steps in the middle) where natives appear and columns and walls fall off. The angle changes to a seemingly new room, but it's obviously the same place, with the camera angle slightly turned to the right. All the previous people are magically gone, the debris has disappeared, and natives are coming out of different places. Really odd editing. (01:30:35)
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.
Continuity mistake: Mutt says, "We have to cross the waterfall," and extends her left hand. From the opposite angle, a frame later, he is extending the right arm.
Continuity mistake: When the Russians arrive at the barrier the sky is either sun setting, bright and sunny, or cloudy, depending on the angle.
Continuity mistake: When Indy finds out that Mac has betrayed him, Mac is standing half a meter away. Right after, from a different angle, he is 10 centimeters away, with the tip of his rifle touching Indy. And right away, from yet another angle, the gun is on top of Indy's shoulder.
Continuity mistake: In the Nevada warehouse,when Spalko is opening the corpse bag, the amount of smoke coming out swaps from a lot to zero depending on the angle, without any logical sense whatsoever.
Continuity mistake: In the Nevada warehouse, the first angle of the corpse's hand shows the baby, ring and middle finger together. When the angle changes, the position of the fingers is completely different, with the baby finger now totally separated from the rest.
Continuity mistake: When Mutt is pulling Indy out of the quicksand both are inches away from each other. A frame later Mutt is meters away in a different position, as if he had fallen backwards.
Continuity mistake: Indy's car crashes face to face against Mac's, destroying its front. When Indy runs away there's a view of the car and the damages are minor.
Continuity mistake: After Mutt falls from the ladder in the graveyard, a native jumps from above to attack him. Indy is already on the right side of the scene, walking out, but when the angle changes he is standing on the left side, very close to Mutt.
Continuity mistake: When Mutt's ladder to the temple ruins breaks and he falls to the ground, the position of the broken parts around him keeps changing positions between shots.
Continuity mistake: In the warehouse, after Indy throws Spalko out of the car he is about to crash against Mac, who grabs the car's window totally panicked. A frame later his hand is away from the window.
Revealing mistake: When Indy's car is about to crash against Mac's, there's a wide angle where the car is seen totally black inside, revealing it's empty.
Continuity mistake: In the graveyard, Indy hits a native with a shovel and knocks his mask and wig off, revealing a short thin hair. A frame later, when the native escapes, his hair is back to fuzzy and long.
Continuity mistake: In the Nevada warehouse, when Spalko opens the corpse's body, its hand is covered in a white dust. A frame later it's clean.
Continuity mistake: In the Nevada warehouse, the way the whip is rolled around the soldier's shoulder keeps changing between angles in a matter of nanoseconds.
Continuity mistake: Indy enters the warehouse and two soldiers on the right gather next to him, while Mac walks towards Indy. When the angle changes, the guards are standing several meters behind, walking towards Indy again.
Continuity mistake: The military car racing against the young kids has its right windshield covered in dust, except for the wiper's track. A frame later the glass is clean.
Continuity mistake: Just before Irina enters the warehouse with her men you can see she has no sunglasses on, as she took them off while speaking to Indy, but as she enters the warehouse we see her remove her sunglasses and hand them to one of her men.
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.