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.
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."