Continuity mistake: At the beginning when Indy is talking to Spalko, his hands keep alternating from being in his pockets to just resting at his sides between shots.
Factual error: During the motorcycle chase seen (which was filmed in New Haven, CT) one can see modern yellow traffic lights covered in burlap in a few of the scenes.
Factual error: In the church, you can see modern brass panic bars on the doors.
Continuity mistake: When Mutt slams his fist on the table in the diner, the ketchup and mustard bottles fall over. When the shot pans to Indiana's back, the bottles are standing up again. He then tells Mutt to sit down and the camera pans back to Mutt. The bottles are lying down again and Indiana picks them both up.
Visible crew/equipment: During the jungle chase, Marion jumps out of the truck, leaving Dovchenko driverless. A few shots later, Spalko fires on the two amphibious vehicles, and when Mac removes his cap to check his head, the actor's modern wired device (earbud or mic perhaps) drops out from under his scarf/shirt and hangs over his shirt. Later, in the chamber with the crystal skeletons, Mac admits to lying about the CIA, then as Spalko climbs the chamber stairs, it looks like her lav mic is a bit visible between two upper buttons. (01:17:10 - 01:44:15)
Continuity mistake: Before Indy finds the crystal skull, the mummy's head has a piece of cloth on its forehead. In a wide shot immediately afterwards, this cloth disappears.
Visible crew/equipment: As they are running away from the ants, you can see a rig of stage lights under the jeep Col. Spalko's crew was driving.
Continuity mistake: When Mutt first shows up, he is riding his bike between two train wagons, or between a train and a railing next to the station. This changes back and forth with no logic at all.
Continuity mistake: When Indiana is with Mutt while the boy rides the motorcycle, Indiana's shoes change; note the soles change from heels to flat rubber-type soles, then back to heeled soles.
Continuity mistake: During the siafu ant attack, while fisticuffs ensue between Indiana and Dovchenko, note the direction of Dovchenko's belt, with its buckle prongs to his left. Then, when Dovchenko falls backwards and the ants swarm all over him, his belt is worn around his waist the opposite way, with its prongs to his right (neither are flipped shots). (01:26:55)
Continuity mistake: At the diner, Mutt places the photo on his hat, yet it swaps from standing out to tucked inside, between shots.
Continuity mistake: At the start, just as the carful of teenagers joins the convoy of military vehicles on the road, there are very long shadows being cast on the road, which vanish in the following shots. Their long shadows return when the convoy turns onto another road, but disappear again as they arrive at the main gate. (00:00:45)
Continuity mistake: At the start, when the carful of teens pulls up alongside the convoy's lead vehicle, in the first shot of that lead driver (his reflection is in the round wing mirror), the side of the hood reads "U.S. Army" and "276***," the partial serial number beneath. Then, in the next shot and subsequent shots, the lead vehicle's serial number reads "1B7731" to the side of the hood. Just to add, when Spalko arrives at Hangar 51, her vehicle has that "276" serial number with license plate W-539. (00:01:05)
Continuity mistake: At Hangar 51, after the Soviets open the crate with the mummified alien, Indiana grabs his whip and secures guns for Mac and himself. In the close-up and wide shot, Indiana is gripping the whip within his palm, but in the next shot, the whip is held with only his index finger; then it's back to being gripped in his palm. Also, while Indiana is aiming the gun at Spalko, the military jeep behind him changes its distance, depending on the shot. (00:13:15)
Continuity mistake: Indy empties the fridge hurriedly and throws away all of the trays, then pulls away the last drawer below. A shot later from a different angle, he is throwing away the penultimate tray and pulling out the drawer again.
Continuity mistake: When Indy exits the fridge after the blast, he leans on both of his arms and faces a gopher. From a different angle, he is leaning on his left arm only.
Continuity mistake: After Mutt's bike knocks down the "Better red than dead" banner it falls sideways; yet when the chasing car arrives, the banner is magically up again, ready to fall horizontally on the car's windshield.
Revealing mistake: During the campus chase scene, Mutt skids his bike and turns left to drive under a stone arch. Multiple skid marks are seen on the pavement from previous shots.
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.
Chosen answer: Because the film had a global release date, and premiered the same day in every country in the world. Obviously, the studio felt this was the best day to do it.
Twotall