The O2 cylinder is still visible in the room even after the "monks" had removed it.
When Rollin, as the Cardinal is sitting in the chair, he is not wearing the rosary beads, however when Zepek looks through the mirror, the beads are around his neck.
During the "tape scene," the tape recorder that Phelps is playing first has a take-up reel that has much more tape than the left-hand reel that is still to play; then in two consecutive shots, there is as much or more tape on the first reel than on the take-up reel; then just before the tape "self destructs," the take-up reel again has more tape than the other reel.
In the closeup, Jim and Cinnamon are being escorted by four monks, however in the wide shot from the balcony, you see only Jim and Cinnamon walking to the front door.
The telephone box that Jim taps into to intercept the call from the monastery to the hospital does not use telephone wire or any logical wiring pattern. The points he taps into should have been adjacent.
When Major Felder takes the impostor's temperature, she reports it as 103. This is obviously Fahrenheit, but by 1968 all European countries were using the Celsius scale (then called Centigrade). She should have reported a temperature of 39.4 degrees.
Just before Jim and Cinnamon drive to the monastery, Jim places a charge on the front tire. In the wide shot of the car, you can see that they are on a dirt road, however when Jim places the charge on the front, the car appears to be on concrete tile floor.
Catholic rosaries are not to be worn around the neck, and most certainly a Cardinal of the church would not do so, but Rollin does this when impersonating the Cardinal. Those he is trying to fool are not true monks, though, of course, so they perhaps would not have noticed the impropriety. However, early in the episode, the true Cardinal is shown wearing the Rosary around his neck as well, so this is indeed a true mistake in the writing and directing.
The panoramic view seen from the monastery is obviously Los Angeles and not the foreign country this is supposed to be set in.
Rollin applies a face mask of the original Cardinal to himself, but had no opportunity to take an impression of the face to make the mask.
When Jim and Cinnamon drive through the monastery gates, you can see a light stand a bounce card reflected in the hood of the car.
Thee is no possible way the IMF team could have known in advance that Rollin would be placed in a sarcophagus in the catacomb, requiring the fabrication of a special tool for his escape.