While Rollin is surreptitiously removing his disguise in the church, he peels off a false left breast pocket from his jacket and tucks it inside. Moments later when he pulls off the false left lapel, that pocket is back on the front of his jacket.
When Qaisette opens the folder containing the information about Jim Phelps, there are two pages in it, both with pictures of Jim on them. In a close-up, Qaisette chooses the paper with Jim's picture centered on it, but in the next shot, we see him holding the second paper with Jim's picture in the upper left hand corner.
When interrogated Barney identifies the hotel as the Metropole, but later when Phelps and Cinnamon are in a car outside the hotel the sign says Hotel Europa.
Barney and Willy escape from prison by using an eyeglass lens with a serrated edge to scrape away the mortar from between the blocks but the lens is not large enough to reach all the way to the mortar on the far side so the blocks would remain in place.
When the tape self-destructs, the smoke comes from behind the tape player.
When Willie and Barney dug out the mortar in the church confessional (into the vault), they were originally shown as digging out all the mortar around the block. When they pulled the block out, it was a very tight fit. Then, when the block is replaced, as shown from inside the vault, the block appears as if it were cut above the mortar joint.
Dr. Holsein told General Qaisette that Princess Celine had bone fragments in her elbow that needed surgery, but when Qaisette examines her arm, the scars are on her forearm.
The close-ups of the tape player show that the tape is in a loop around the two reels. The inner part of the reel toward the back is silver, indicating there is no tape being wound. Also, the tape returning to the front reel is visible in the close-ups.
Considering Barney's dexterity and precision, when he is manipulating the puzzle box, a bruise can be seen on his left index finger, indicating that at some point, either on set or off, some heavy object accidentally came in contact with it.