As Dr. Angelo is telling Caroline that she doesn't understand what he is going through, he rubs his eyes with his empty left hand in close-up. In the next shot, a cigarette has suddenly appeared in his hand as he pulls his hand from his eyes.
Dr. Angelo, remarking on Jobe's progress with Latin, says that he himself took a year to learn just the Latin alphabet, which is still in use, plus a few letters, as the English alphabet. (In mitigation, he could be referring to the difficulty in reading ancient manuscripts, or how long a child takes to learn how to read, though this seems unlikely in context.)
When Timms is upbraiding Angelo for being naive, he says that money has been dirty "...since the Catholic Church got involved in banking 300 years ago." But in fact, the Knights Templar (an arm of the Catholic Church) first began banking in 1129 A.D. Timms was off by 600 years.
The goof item below may give away important plot points.
After Jobe uses his telekinetic ability to force the rifleman to shoot himself, a device on the back of the head of the actor playing the shooter (used to spray fake blood on the wall behind him) can be seen as his body falls.