
Visible crew/equipment: After Marion supposedly dies in the truck explosion and Indy is drinking outside at the bar, watch to the left of him. You can see a man wearing a modern t-shirt and jeans walking through the crowd. (00:42:20)
Suggested correction: This is probably the most famous non-mistake of all time. Denim jeans date from 1871. They were first sold by Jacob Davis and Levi Strauss in 1873 and the design hasn't changed much since then! Plain white cotton T-shirts date from 1898 and were first issued by the US Navy to their sailors in 1913. The design caught on immediately and they flew off the shelves. In short, there is nothing at all unusual about a man wearing jeans and a T-shirt in the late thirties.
He's the only person wearing that outfit in Cairo. Every single other person is wearing "traditional" clothing. He's clearly not meant to be in shot.
He could have been one of the few American tourists in the area.
Noman
If that's true, then what about the two guys standing in the door/archway and the one guy who is sitting in the doorway next to them - all three of them don't match the rest of the extras either? (all three are in the background to the left of Indy before the supposed blooper guy appears and walks right in front of them during the scene).
"There is nothing at all unusual about a man wearing jeans and a T-shirt in the late thirties." However there is a good deal unusual about a caucasian man in jeans and a tshirt in cairo in the 1930s. He is entirely out of place.
Unusual does not mean impossible, and in order for him being there to be a mistake it has to be impossible. It isn't. Unlikely is not impossible. This is not a mistake.
That's not how it works. Say someone is wearing a jacket, is off screen for 4 seconds, then cuts back and the jacket is gone. It's technically possible they ripped it off themselves in 4 seconds on a whim, but that's not actually feasible. There's one solitary man in jeans and a T-shirt in Cairo in the 30s, when every single other person on-screen is wearing different clothing. The most likely explanation is it's a screwup.

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 man with a white sleeveless shirt and a big brimmed hat all in the reflection of the glass. (01:18:20)

Visible crew/equipment: When Indy and Sallah are deciphering the head piece there is a shot over Indy's shoulder. As he turns you can see the reflection of a fluorescent light in his glasses. (00:48:40)
Visible crew/equipment: When Indiana is chasing the Nazis in the truck, look closely at the convertible, you can see the camera on the windshield. (01:23:25)

Visible crew/equipment: As they come out of the "mapping room" in the tomb, there is an extra crouched down by the door, apparently hiding. It seems as if it was a quick fix for someone who was where they weren't supposed to be.
Suggested correction: It's a man, who was punched by Indy in a deleted scene. He is lying still and not crouching at all.
Visible crew/equipment: When Indiana is thrown through the windshield of the truck during the truck chase scene, there is another man in the driver's seat leaning toward the door, driving the truck with dark hair. This is noticeable just as the glass is broken.
TD9898Visible crew/equipment: As the bad guys are leaving the dig site for Cairo, there is a shot of the black vehicle (lead car) looking right at the driver. On the bottom of the shot is a shadow of film equipment that shouldn't be there. The shot lingers, so the shadow is very visible. (01:22:50)
manthabeat
Visible crew/equipment: At the beginning of the ark chase sequence, Indy jumps into a truck off a horse and fights the driver. He pushes the driver up against the door. At the bottom of the frame you can see the camera shadow. (01:23:35)
manthabeat