
Continuity mistake: The position of the Top Secret sign and the whole text is put on the ark's box across vertically laid planks, with a wood crossbar on the right, which only the side panels have. A shot later the sign appears slanted across horizontally laid planks. Though it could be argued that there could be a second sign on the opposite side with horizontal planks, when the warehouse guy turns left to store the crate, we get a glimpse of the left side and it's not painted.
Suggested correction: The other text and the different plank design could be on the base of the box or on the front wall (the wall opposite the man pushing the box), two walls we never see when the box is being pushed. In fact, at one point the camera passes next to a box that has two texts, one on a short wall and one on a long wall.
Continuity mistake: After Satipo runs with the idol, Indy grabs a root to help him climb up the ledge. Half a second later, from a different angle, the root is meters away and he is grabbing it again, repeating the whole scene.
Continuity mistake: Just before the car carrying Marion in the wicker basket explodes in the alley, Indiana shoots a man twice in the chest. The man has blood stains on his shirt before he is shot.
Continuity mistake: At the beginning of the film, When Indy uses the whip to take the guides gun away, Satipo makes a weird face and starts to move away in amazement. The very next frame, in a wider shot, he is not finishing his movements, but on the contrary he is standing still, with a normal gesture, until a second later he starts to repeat the movement and looks from before.
Continuity mistake: As Indy and Marion are starting to run from the plane, you can see the yellow wheel chocks are back in place under the plane's tires.
Continuity mistake: After hitting one thug, Indy jumps out of the way of one trying to spear him, leading to the one behind Indy getting run through. As the guy gets run through, he is in front of a hanging string of fruit, with the stacked fruit to his right. After a cut scene to Indy and Marion running away, the run through thug is now facing the fruit stand, setting up the sight gag of the blade sticking out with two fruits stuck on it.
Continuity mistake: While Indy is in the Well of Souls, Belloq greets him and is standing by one of the four sides of the rectangular hole. A frame later he stands by one of the corners.
Continuity mistake: Satipo drops the whip half a meter away from the closing gate, then runs away. However, when Indy rolls underneath the door, the whip is laying right next to it.
Continuity mistake: When Indiana is hiding his face with the cloth, watch as he enters the tent that Marion is being held prisoner in - at first, Indiana has to hold it in place; in the next shot, he has it tucked into the rest of the folds. The next shot, the actual position of the cloth changes.
Continuity mistake: When Indiana is fighting the Big German mechanic by the plane, the plane goes around in circles and the wing tip of the plane punctures a hole in a petrol tanker that is parked near by. This causes the petrol to gush out of the tanker and you can see that ground underneath the plane gets totally drenched with petrol. But in the later shots, the ground under the plane is dry. There is also a shot where you can see the tanker in the background not pouring petrol any more and all you can see is a little wet spot around the tanker. (01:18:45)

Continuity mistake: After Indy replaces the idol for a bag filled with sand, the position of the bag changes between frames.
Continuity mistake: In the map room, after Indy has discovered where to put the stick in, the sun rays lights the head and shoulder of a painted figure and the whole body of the figure to the right of it. A frame later the first figure is now completely lit. Too fast a change.
Continuity mistake: When Belloq talks to Indy in the Well of Souls the two Arabs on the left disappear in the angles from Indy's POV.
Continuity mistake: After Indy rips a big strip of Marion's dress in the Well of Souls, it continues to change until she finally gets rid of it on the boat. At some points (eg. running from the plane before it explodes, and other shots) it seems quite straight across, more like a shorter dress than a torn one. A few moments later, when they are crouching behind an earth bank and Sallah tells Indy the Germans are putting the Ark on to a truck, the dress is badly ripped in various places across her back. Not long afterwards, it is in one piece again but back to the bottom edge being ripped. (01:13:00 - 01:21:35)

Continuity mistake: When Indy climbs onto the pontoon of the airplane from the lagoon in the opening sequence, he is obviously wet from swimming in the lagoon. However, in the next scene as he climbs further, his clothes are miraculously dry as observed by watching them blowing freely during take-off. (00:12:05)

Continuity mistake: Indy looks at the Wurffler through the binoculars. In the next shot, when he takes them off and looks at Katanga, the submarine has moved to the left and astern. (01:34:58)
Continuity mistake: During the shooting at the bar, Marion covers her ears to muffle the sound, but a frame later they are around the wall in front.
Continuity mistake: Indy climbs on a plane's wing, and a German mechanic arrives and asks him what he's doing, raising his left arm and ordering him to approach. A shot later, the arm is down.

Continuity mistake: When Indy and Brody meet at the University with the two government officials, a group of rolled maps or plans are placed on a podium horizontally. Halfway through the scene, they are all laying vertically.
Continuity mistake: After Indy steals the idol, while he is hanging in the well, in the front angle his left leg is bent and already outside, in a quite comfortable and secure position; yet in the angles from behind both legs are inside, hanging loose.