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.
Continuity mistake: When Indy and Mutt's bike is about to exit the campus, a green car is passing by, which disappears in the immediate wide angle of the street.
Continuity mistake: When Mutt and Indy ride inside the arched door in the campus, a couple runs away, yet appears still there from the opposite angle.
Continuity mistake: When Indy and Mutt are about to enter the university, the guard is holding both gate doors almost closed. A frame later he's holding one completely opened.
Continuity mistake: When the Akator temple starts to move, the sand by the groups' feet keeps changing from sandy with a couple of rocks, to filled with weeds and leaves, and back to sandy.
Continuity mistake: Inside the waterfall temple, the group walks by a room (with a passage on each side and a double entrance with steps in the middle) where natives appear and columns and walls fall off. The angle changes to a seemingly new room, but it's obviously the same place, with the camera angle slightly turned to the right. All the previous people are magically gone, the debris has disappeared, and natives are coming out of different places. Really odd editing. (01:30:35)
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: 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: 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: 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: As Indy's truck is getting closer, the camera focuses on Spalko. Behind her are the duck with Oxley and Mac inside and a damaged truck. But in the next shot, when Oxley says "Henry Jones Jr.", the truck is gone. (01:16:17)
Continuity mistake: Before being knocked by Mac, a Russian soldier throws the Skull to Spalko, who has her rapier in her right hand. In the next shot, the rapier is in its sheath. (01:18:48)
Continuity mistake: When Spalko is trying to throw Indy's car off the cliff, the knocked-out soldier in the passenger seat of the amphibious car is suddenly conscious and sitting between shots. (01:22:30)
Continuity mistake: After Mac knocks the Russian soldier out of the car, the position of Oxley's head and arms changes in the next shot. (01:18:49)
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