Factual error: At the beginning of the movie where the convoy stops at the gate to the military base, the fence has "Razor Wire" on the top, not the period-correct barbed wire. Razor wire came into use in the late sixties by some industries, but the military did not use it until the eighties.

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.
Factual error: In the wedding scene, the minister uses the modern, politically correct "I now pronounce you husband and wife" instead of the traditional "man and wife" - unheard of in 1957. (01:54:50)
Continuity mistake: When the civilian car escapes the oncoming car, the three trucks of the military convoy are missing. Only the three small vehicles are on the street. (00:01:25)
Continuity mistake: When Spalko climbs a hanging vine to escape the large, marauding ants, one jumps on her leg. As it crawls up, she smashes the squishy bug between her knees (you can hear it splatting), but there's no stain or body parts left on her very clean pants.
Continuity mistake: During the scene where Indy and Mutt first find the skull and they are having a conversation about it. Indy is holding the skull with the face pointing to his right. As the camera changes back it is facing to his left, then it changes back again.
Continuity mistake: When Indy is held captive in the Soviet's tent, Mac enters and they have a conversation. Indy then turns his head to his left, looking straight at Mac. Just before Indy makes his threat about what he'll do to Mac when he gets loose, there is an angle change, and Indy is suddenly staring straight ahead, with no time to turn his head in between shots. He then turns his head back to look Mac in the face again.
Continuity mistake: In the beginning when Indy's hat is thrown from the trunk onto the ground, it faces the 9 o'clock postion. But when Indy reaches to pick it up half-a-second later, it faces the 12 o'clock direction.
Continuity mistake: Indy's mostly buried in the quick sands and he is handed a snake. Half a second later, when he has just managed to grab it he isn't buried as deeply.
Visible crew/equipment: After everyone has fallen into the water beneath the obelisk and the skull has been retrieved, Indiana is leading everyone out of the water and a prop light can be seen on the big rock spike behind Mutt. (01:40:25)
Continuity mistake: Indy's head position and hairstyle keeps changing in the shots after the test jet comes to a stop.
Continuity mistake: Throughout the whole movie, Irina's hair seems to be kept absolutely pristine, even when she is flung from cars. This is very noticible at the car chase in the military base when she is thrown from the car by Indy. One minute, a few strands of hair are slightly messed, then they are fixed again. It is likely, however, given the many other nods to films of that period, that the "concrete hair" effect is a deliberate decision.
Continuity mistake: In the diner scene between "Indy" and "Mutt," Indy's shirt-collar points are smooth under his jacket lapel in some close-up shots, but in others one collar point is curled up.
Continuity mistake: In the university classroom scene, Indiana turns to the dean and says, "Yes?" He is holding the chalk with both hands and his elbows are bent. In the next shot, both arms are at his side. This is seen on the DVD. (00:25:00)
Continuity mistake: During the wedding scene, we see Mutt taking photos with a 1950s Kodak Brownie box camera. When wind blows Indy's fedora off the hat rack and up the aisle, Mutt stoops to pick up the hat, with the camera no longer in his hands. Indy snatches the hat away from Mutt as he passes, and the shot then cuts to a full view of all the wedding guests leaving the church, with Mutt in the center of the shot, still standing in the aisle the whole time. He takes out a comb and passes it through his hair, then picks up his jacket from the pew before he leaves, but the boxy Brownie camera is still nowhere to be seen. It's not in his pockets, and it's not in his jacket (the angular bulge would be more than noticeable).
Audio problem: When Irina and Mutt are sword fighting in the jungle, the blade strikes all make echoing sounds.
Other mistake: Spalko is hanging from a tree to avoid the sting of the ants. When a CGI ant is on her knee she closes both legs and smashes it. If you watch closely you'll notice that when she closed her legs the ant was already over her thigh, so if it had been a real ant it would have been impossible to kill that way.
Factual error: The Russian soldier would not be able to scream with ants running into his mouth - he would be choking.
Other mistake: In the scene when they are all inside the temple with the skeletons, the Russian woman takes the skull and walks up the stairs directly in front of the creature. Yet there are no direct steps. All steps leading up to the skeletons are a little off to the left and right, and there are two sets of them.
Character mistake: In the scene with the ants, Jones refers to them as "Siafu", which is actually the Swahili name for driver ants which are native to Africa, not South America.