Continuity mistake: When Indy and Mutt exit the bar, there's a man and a young girl close to each other, plus a man in brown 4 metres behind, running towards them. A shot later, the man and girl are a metre apart, and the man in brown is right next to the young girl. Also, the man in a gabardine that walks by when Mutt gets on his motorbike has no continuity between shots.
Continuity mistake: After they fall inside the temple, Mac steals gold from the skeleton and turns around. Shot changes, and he is turning his back on us, repeating all previous movements.
Factual error: Skara Brae is on Mainland Orkney not the West Coast of Scotland as Indy states in class just before he's let go from the university.
Continuity mistake: When Indy tells the group to run away from the ants by jumping off the truck, Mutt jumps out, followed by Oxley. Shot changes, and Mutt is back in the truck, and Oxley is already out.
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.