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: After Indy has been decontaminated, the lamp behind him swaps from lit to unlit between shots.
Continuity mistake: While Mutt's bike is sliding along the library floor, right before it comes to a stop it's pushing a chair on the right. A frame later the chair has magically made a 180ยบ turn and moved half a meter to the right.
Continuity mistake: When Indy and Mutt are in the diner, two baddies show up, Mutt pulls out his knife and places it leaning to the left. In the close-up it's facing upwards, despite Mutt not having moved it.
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: After Mutt crashes his bike in the library there's a shot on a nerd. Watch the table behind him. A lamp suddenly appears in the second angle.
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.
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: During the credits, while the young kids are racing the military car, the jeep behind always has a roof, as seen in all the outside and inside angles. However, in barely half a second, when the cars turn towards the base, the jeep has no roof.
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.