Ellie Andrews calls Peter by his name at the terminal before she actually knows it. In a later scene, she asks him what his name is.
When Peter is making breakfast for Ellen, as the table is first set, there are six doughnuts on the plate in the lower left corner of the screen, but when they sit and begin eating and discussing what there is to eat, there are only two.
As Peter is singing and threatening to take off his pants, Ellie begins to bolt behind the hanging blanket. A half second later there is a shot of Ellie looking at him for a solid second, and then bolting to the other side of the blanket.
In the exterior view of the bus running off the road (after the "flying trapeze" song), the driver is a different person and the curtain that is behind him in the interior view is missing.
When Peter is explaining to Ellen how he gets undressed they show him in a frontal shot and Ellen is leaning with her back against the wall watching. When he gets ready to take his pants off she gets scared and starts to leave coming forward off the wall. Next shot is a frontal of her and she's back against the wall and starts to leave again.
Andrews bellows to Westley on the phone: "Hello, my would-be ex-son-in-law." Until the annulment is finalized, Westley remains Andrews's son-in-law.
The bus as seen from the inside is wider than as seen from the outside.
In the closing scene, the manager has given Peter a trumpet. We hear him play it, but the last 3 notes he plays are clearly three trumpets playing in harmony.
After King lands and taxis in the autogyro, apparently the sole occupant, a man is visible in the cockpit crouching down as King walks around and to the rear of the autogyro.
In the opening scene, Daddy's yacht is supposedly anchored off Miami. Yet in the distance are tall coastal hills, similar to what one might see in Southern California. Such a topographical feature is unknown in South Florida.
When Warne is chasing Ellie's convoy after she's been picked up "outside Philadelphia," a road sign is visible reading "California U.S. 101."
When Peter is held up by the train at a crossing, the caboose is plainly marked SP (Southern Pacific). But he is supposed to be in New Jersey. Although there might be SP box cars in New Jersey, there would not be an SP caboose.
Ellie Andrews flees Daddy's yacht by jumping overboard and swimming to shore. She is clad only in a nightgown and presumably has no wallet, money, nor identification, yet she somehow acquires traveling clothes and money to pay for a bus ticket while dodging Daddy's active search for her.
The note Peter sends Andrews does not contain his contact information, yet Andrews telephones him.
At the end of the movie an annulment is mentioned. An annulment would not be necessity since the wedding ceremony was not completed as the bride left in the middle of the ceremony. Presumably the marriage license between them had not yet been signed.