Continuity mistake: At the beginning of the movie, Ted Grossman runs away. Then Indy, Satipo and Barranca enter the scene. In the next shot, the position of Satipo's arms has changed. (00:01:38)
Continuity mistake: Belloq, Dietrich, and Gobler arrive next to the destroyed Flying Wing and begin to walk towards the intact wing, while Dietrich says, 'Have it put on the truck.' In the next shot, the Flying Wing and the entrance to the Well of Souls have disappeared from view (instead of the latter, you now see the hut where Pat was). In addition, some barrels suddenly appear between shots, next to which the three antagonists stop. (01:20:59)
Continuity mistake: Just as the ghosts fly out of the Ark, a soldier can be seen on the left side of the altar, with nothing in his hands. Two shots later, that soldier is now carrying a banner.
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Continuity mistake: As the ghosts dance around the pole to which Indy and Marion are tied, large clouds can be seen in the sky behind them. However, after a ghost circles Dietrich and passes in front of the camera, it can be seen in the background that the clouds behind Indy and Marion have disappeared.
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Continuity mistake: As the ghosts dance around Dietrich, Belloq, and Toht, the Frenchman slowly looks up as the column of mist ascends upwards from the Ark, almost looking straight ahead. In the next shot, Belloq is looking down again; the shape of the mist has changed, and the column of mist is now moving to the right.
Continuity mistake: When the portal opens over Geheimhaven, you can see that in the sky and inside the portal there are a lot of blue clouds. Two shots later, in the shot inside the portal when the fire turns on itself, the clouds have disappeared and the portal's interior is now the normal night sky (black and with one star visible).
Continuity mistake: When the Ark is 'sucking' all the fire, the klieg on the left of the screen points towards the altar. Two shots later (and after the Ark closes), that klieg points towards Indy and Marion.
Continuity mistake: In the Well of Souls, Indy and Sallah place the Ark in the box. Indy closes the box with a wooden lid and looks up. In the next shot, a torch has appeared in Indy's hand, a rope has appeared, tied to the four sides of the box, and Sallah has appeared next to Indy's left shoulder. In addition, the box is already several metres above Indy and Sallah in the second shot. (01:09:43)
Suggested correction: There is an obvious time jump between the shots. They simply decided not to spend ten minutes showing all the details of sealing the box and tying the rope around it.
I wouldn't say this was a deliberate time jump, as they show Indy carefully and slowly placing the Ark in the box, then sealing it. In addition, when he looks up, he immediately says, "All right... take it up! Easy!" so it's clear this is a continuity mistake.
He says, "All right. Take it up." After the cut. Yes, he does look up before the cut, but since everything else is different, we are supposed to interpret it as a jump in time.
In fact, almost nothing changes between these two scenes, except for these small but clear details.
There's a deliberate jump in time between these two shots, and this transition is done creatively. First, we're below with Indiana as he places the lid on the crate and looks up toward the top entrance; it then cuts to the entrance POV, and now we're looking down as the tied-up crate is being lifted. The jump in time between these two shots is transitioned using a type of match cut. Absolutely no mistakes regarding these two consecutive shots.
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Continuity mistake: When Indy goes to save Marion in the tent he removes the handkerchief gag. But when he decides to leave her there, he puts the gag back on and some of her hair gets caught underneath the gag on one close up shot from the left. But when the camera goes to the back of Indy, her hair is no longer caught underneath the gag. (00:56:00)
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Continuity mistake: Near the beginning of the movie where Indiana is running away from the tribe of South American Indians after Belloq robs Indiana of the gold statue, in one shot you can see that the Indians are only a few meters behind Indiana, but in the next shot, they are at least 50 meters behind. (00:11:20)
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Continuity mistake: Before the shoot-out in Marion's bar, before the Nazis enter and ask her for the amulet, she's sitting alone at the table. She pulls the amulet out of her shirt, the chain still around her neck, and stares at it in the candlelight. The next moment the chain is not around her neck and she hangs the necklace onto the table centrepiece. (00:28:20)
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Continuity mistake: When Indy is distracted by the young girl and her eyelid message, the girl changes from a window seat to another row when the bell rings to end class.
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Continuity mistake: In the Himalayan bar scene when the sherpas leave, Marion starts to pick up the shot glasses and puts them on a tray - there's a large group left at one end of the table, one in the middle, and two by a bowl at the other end. When she returns for the rest, the two by the bowl have vanished. (00:26:20)
Continuity mistake: When the village crowd separates and reveals a standoff between Indy and the black-robed swordsman, the rear shot of Indy shows his hip-bag to the rear of him, the frontal shot of Indy shows his hip-bag on the forward part of his hip.
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Continuity mistake: When Belloq is talking to Indy and Marion in the Well of Souls, he's shown holding his hat with his right hand. But in the only over-the-shoulder shot (looking into the Well of Souls) the hat is laying on the ground and Belloq tosses a stone down with his right hand. Then the hat is back. (01:10:35)
Continuity mistake: Marion's bar in Nepal is built with thick stone walls, but after the fire, all you see is the burned-out shell of a wood-frame building.
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Continuity mistake: Just after Indiana (barely) escapes the tumbling boulder at the beginning of the movie, he leaps through a veil of spider webs, only to be held up by the native hunters and Belloq, who takes the idol from Indiana. Watch carefully - there is a thick strand of webs attached to the idol as Indy hands it to Belloq, but they disappear in the next shot as Belloq hefts the idol and holds it up in the air.
Continuity mistake: When Indy and the Peruvian are entering the cave and clearing the cobwebs, you can see at least one spider on Indy's back. The next shot shows a clear, long shot of Indy's back with light reflecting on his jacket and no spiders. In the next shot, the Peruvian notices the spiders. (00:04:20)
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Continuity mistake: When the government comes to see Indy at the University he is teaching, they enter the large room, I think it's a gymnasium. He puts the huge book on the table and one of the buckles comes undone. But when he goes to open the book to show the g-men a picture of the Ark he undoes both buckles. (00:15:30 - 00:19:30)
Continuity mistake: At the beginning of the film, Indiana Jones uses his whip to disarm a man with a handgun. The scene showing this action includes several quick shots, but as a result of the use of these multiple shots it can be seen that the whip descends twice. (Slow motion helps, but isn't required.)