When Anne tells Bert to sit next to her while they are scoping the clientele at the big city hotel, she is smoking a cigarette. But on the following shot when Bert moves next to her; she is not smoking nor is there a lit cigarette.
Bert goes to a jewelry store to purchase something as a scam to get his $5,000 back. He buys a bracelet. Later when Anne asks Bert where did he get the money for their train tickets, he says he bought a necklace.
While in the car on the way to the racetrack, Dan hands Ann the money twice between shots.
At the start of the movie, a hotel elevator is indicated moving up more than three floors in one second - an impossibly fast speed, even today. Its return down is shown at a more realistic pace.
On close inspection of the handwriting, it's evident that both "Darling, paste this..." notes were written by the same person. Not necessarily. Handwriting was a far stricter subject in the early 20th century, with an emphasis on conformity, and both notes were written in the standard font for Americans at the time. Anyone who "did well" in handwriting in public schools had basically that same handwriting.
After Anne Roberts breaks the pearl necklace in reaction to the hotel guests' flirtation, the pearls scatter all over the floor and the dresser. In addition, she takes a handful of pearls and pours them down his pants. The number of pearls on the necklace before it broke could not possibly equal the large amount that scattered all over the room and that went down his pants.
There's no wind on the actors when they are supposed to be riding in a convertible with the top down. No one's hair or hats move, and Blondell's hat even has a perfectly-still feather in it.
Twice the con man/driver is shown calling to get the horse race winners from a phone booth. However the phone booth both times is exactly the same although it is supposed to be in different locations.
The W/C (if indeed it is such) in the jewelers room had only a sink in it. Although it is not uncommon even today for hotel rooms to have only sinks in them with a communal W/C on the same floor, it does not make sense for there to be a separate room even partitioned off with a door if it only has a sink in it.
When Bert is in the car chase, they pass a Three Owl drug store, which was a West Coast chain, despite the scene being set in New York City. Other advertising also points to California: a See's candy store and a neon sign for Motorite motor oil from the Union Oil Co.