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.
Corrected entry: When the Nazi soldier is killed by the airplane blades, some of his blood splatters on the pilot cabin glass where Marion is, but in the next shot, the blood has totally disappeared from it. (01:20:24)
Correction: This is incorrect. First, the blood splatters on the gunner's turret cabin glass, not the pilot cabin one. Second, Marion crawls from the gunner's turret cabin to the pilot cabin, where there is no blood. Also, this last point is not shown exactly in the next shot, as this mistake suggests.

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.
Factual error: At the beginning of the movie, Indy escapes in biplane with registration OB-CPO (a Star Wars nod, as noted in trivia). However the OB registration is used by Peru, and it should be followed by four digits, not by three letters. (00:12:10)
Suggested correction: Simply not true, as with most countries with two-letter civil aircraft registrations, Peru used the XX-YYY format at this time: http://www.airhistory.org.uk/gy/reg_OA-.html.