Revealing mistake: While Indy and Marion are in the Well of Souls, and they encounter the snakes, Indy falls to the ground only to be confronted by a hissing Cobra rearing its head. Look carefully and you'll see the snake's reflection on the safety glass between it and Indy. Briefly you can also see the torch's reflection while he's waving it around. [This has been corrected in the new DVD set. You can only see it if you have the original VHS. I think it's visible in the "making of" on the DVD as well.]
Revealing mistake: When Indy fights the driver of the Nazi truck, he gets thrown through the windshield, and eventually ends up underneath the truck. When he is climbing underneath the truck, heading towards the back of it, you can see the trench that was dug down the middle of the road to provide the stuntman (this being one of the few stunts that Ford didn't do himself) with the extra room needed to do this feat. (This is backed up by DVD commentary. The director stated that the truck was too low to the ground so they had to dig the trench in order for there to be enough room for the stuntman).
Revealing mistake: When Indy jumps across the pit to pursue the spy that took the idol, he barely makes it across, grabbing the ledge on the opposite side with his hands. When he pulls himself up, he kicks loose a rock and the entire "solid" rock wall shakes like it's nothing more than a foam wall.
Revealing mistake: After Indy gets behind the wheel of the truck containing the ark, he jerks the steering wheel to the right to run the pursuing jeep off the road. He then jerks the wheel to the left to hit an upcoming motorcycle. In neither case do you see his body sway with the presumably drastic swerve of the truck. Apparently this was filmed in a stationary vehicle, or one in tow that was fitted with a prop steering wheel.
Revealing mistake: The Pan American aeroplane Indiana Jones boards in San Fransisco looks similar to (but has noticeable differences from) the Boeing 314 PanAm used for transpacific flights. This aeroplane did however not fly until 1938 and at the time of the story the company only flew transpacific with Sikorsky S-42s, an aeroplane with a completely different body than the one used in the scene.