Continuity mistake: In the taxi, they almost hit a large truck coming toward them. Cary Grant taps the driver on the shoulder, and they miss it. The very next shot has the rear window of the car in it. The truck has disappeared.
Revealing mistake: Cary Grant shows off his ice skating moves but you can tell it's a stunt double. The double is a bit shorter than Grant. Also in the same sequence, the two other skaters have noticeable doubles as well.
Character mistake: In the final sermon, Henry says "Uncle Henry" instead of Uncle Harry - as shown in the earlier typed sermon.
Continuity mistake: When Dudley drafts the sermon he says "you give me a tie, I give you a book." When the bishop reads the sermon he says "you give me a book, I give you a tie."