When Doris Day puts on her black evening gown near the beginning of the movie, she has on a black slip with straps. She adjusts the straps of the gown over the straps of the slip. Later, when she and David Niven are eating dinner in a restaurant, the strap of the dress slips off her shoulder, and there is no slip strap.
The volume of water in the enema bag changes from scene to scene. The bag is less than a quarter full while they are filling the paper bags and when they start to empty it into the potted plant. Then it is more than half full a few seconds later in the next scene.
When Larry reads and critiques Joe's play, he comments on the setting being in "Jerusalem" and a leading character being "Father Abraham." The city of Jerusalem was not a home to the Hebrew people until several generations beneath Abraham, specifically at the time of King David. However, this could be intentional, in order to demonstrate the amateurish writing of a cab driver.
When the cab driver turns around to shake MacKay's hand, he almost has an accident and jerks the steering wheel quickly to his right - but the scene through the cab's rear window doesn't move sideways at all.
When Kate is playing the song for the children in the schoolyard, her strumming of the ukulele does not match match the music.
A slap from a gloved hand, as Ms. Vaughn gives to Mackay at 25:15 and 25:28, does not make that sound.
When Kate Mackay (Doris Day) is putting on her makeup at the beginning of the film, she tells the boys "Oh fellas, now you know I have to meet David-" and stops mid-sentence. She should have used Larry, Laurence, Dad, or some other character reference rather than the actor's (David Niven) name.