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.
Continuity mistake: The CCCP emblem on the back of Irina Spalko's uniform appears and disappears between shots, most notably when she is descending off the cliff and we get a clear view of her back-minus the emblem.
Continuity mistake: When Col. Spalko begins cutting the leather covering the alien corpse in the casket, no straps are seen. In the close-up shot a strap is suddenly visible.
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.