Other mistake: One of the soldiers at the table Sallah and Indy walk next to, is only pretending to eat with his spoon. (00:54:53)

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: Sallah and Indy are peering into the well of souls. Sallah is to the right of Indy. Indy then drops the torch into the well, and when the camera comes back up, Sallah is on the left of Indy. (01:00:00 - 01:00:45)
Suggested correction: Indy and Sallah spent several seconds off-camera, enough to move around the hole and switch places.
Audio problem: When Marion and Belloq are getting ready to have a drink, as Belloq pours the wine you can hear the sound of the wine hitting ice, making a crackling sound, but there is no ice in the glasses. (01:04:40)
Continuity mistake: When Toht frees Marion's arm, Dietrich enters the tent, and a few seconds later, Gobler enters. In the next shot, Gobler enters first, with Dietrich second. (01:07:52)
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.

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)
Other mistake: In a shot of Belloq speaking to Indy in the Well of Souls, in some shots of the Desert Chase (such as when Belloq shouts Allah va!) and when the three villains enter the submarine with Marion, Wolf Kahler's double is seen, who has black hair. (01:10:43 - 01:24:42)

Continuity mistake: Dietrich and Gobler walk forward to stand next to Belloq while he's saying, "Once again, Jones..." In the next shot, Gobler has disappeared (this can be spotted by the distance between Belloq and Gobler's foot in the first shot). (01:10:57)
Revealing mistake: When Indy and Marion are being sealed up in the Well of Souls, You can plainly see Marion counting down (she is mouthing the numbers) to the cue for her to scream as the Well is sealed. (01:12:20)
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 Indiana is climbing the statue to escape from the Well of Souls, the snake he encounters makes a rattling sound. However, the snake has no rattle and rattlesnakes are indigenous to the Americas. (01:13:40)
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)

Continuity mistake: The stone block Indy pushes out to create an opening which allows him and Marion to escape the Well Of Souls apparently rolls down the hill outside. We see it, in a following scene, laying about 15 feet away from the Well. But when Indy is fighting the big German guard near the airplane, one scene clearly shows the Well in the background and the dislodged stone is now laying on the hill only a few feet from the opening. (01:15:45 - 01:18:10)
Character mistake: When Gobler informs Dietrich about the preparation of the Flying Wing, the former calls the Colonel "Herr Major." (01:16:25)
Factual error: When Indiana Jones is fighting the big German by the airplane, the German punches Indiana Jones on his right cheek. Indy's face and body are both knocked down to the right, in the direction of the punch. When you watch this, you can see it's impossible to be knocked down in such a way. (01:17:55)

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)
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)
Revealing mistake: When Indy is fighting the big German at the plane, if you look at the wheels when the plane is turning around, you can see a chain and sprocket assembly that is driving the wheel to actually turn the plane. (01:18:55)

Visible crew/equipment: When Indiana frees Marion, locked in the cabin pilot of the Nazi plane just after one of the soldiers is killed by the blades, a set light is reflected on the plane's glass. (01:20:32)