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)
Other mistake: When the fire is falling into the Ark, one shot before it closes, two lids can be seen at the same time. The first is on the floor of the Altar, with the two golden angels on the lid being very visible (the one on the left is the most visible), while the second lid is the one falling from the sky.
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: 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.
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.
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.
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 Nazis board the Bantu Wind, there are some shots of the pipe Indy is hiding in. During these shots, there's a big grey pipe right behind Indy's pipe. However, in the rest of the Bantu Wind shots, this grey pipe is on the left of Indy's pipe, not directly behind it. (01:36:19 - 01:37:05)
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. You can also see Marion's reflection when she falls in later on and is face to face with the cobra. [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.]
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)
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)
Visible crew/equipment: As soon as Marion gets locked in the cockpit of the Nazi plane, you can see a crew, a blue van, a ladder, and a crew member with a white sleeveless shirt and a big brimmed hat, all in the reflection of the glass. (01:18:20)
Revealing mistake: Watch the shadow of the stone Indy pushes out to escape from the Well Of Souls - it bounces down the sand dune, exactly the way a large rock shouldn't. (01:15:30)
Plot hole: When Indy and Sallah visit the gentleman who translates the staff headpiece for them we hear the staff should be "six cadams high." Indy replies, "About 72 inches." Then, turning the headpiece over, "Wait - take back one cadam to honor the Hebrew God whose ark this is." It's definitely referring to the staff length - Indy says afterwards "Their staff is too long." So, about five feet now, right? But, when Indy goes to the map room the staff is much taller than him. If the staff is about five feet high, Indy would be around three feet tall. (00:48:25 - 00:53:05)
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)
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: 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). (01:27:50)
Factual error: The film starts in the year 1936, and just like the RPG Indy uses to threaten Belloq with, the MP40s (or at the earliest, MP38s) are an arms-historical anachronism in this movie. As the numbers in their names imply, the MP38 was first produced in 1938. The weapons in the movie are not the similar-looking ERMA MP-36, you can see the ribbed, vertically angled magazine holders typical for the MP40 - its predecessors had either a 30°-canted, smooth magazine holder (MP36) or a round viewing port for checking the ammo (MP38). (01:31:45)
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.
