The guests at the 1904 wedding are the same people, wearing the same clothes and hairstyles, as the guests at the 1944 wedding. Of particular note are the young girl wearing a giant red flower as a hat, and the white-haired old lady with white boa feathers on the side of her head.
Maurine pins the VANITY cover photo of Rusty on the call board in a wide shot, but it is a different picture from the next cut- a close-up of Rita Hayworth's face. When they cut back and forth to the wide shot, the difference is so startling that it does not look like Rita Hayworth at all. The faces even tilt in opposite directions.
Just before Danny and Rusty talk for the first time about her being a cover girl, Genius is called on stage to do his "Who's Complaining?" number, yet the music playing in the background is "Long Ago and Far Away." Also Rusty isn't in her cab driver costume.
When Rusty's face appears on the cover of a top fashion magazine, someone rips the cover off and there is no ad on the reverse side - traditionally (along with the back cover) one of the most sought-after pages for magazine advertisers.
The goof item below may give away important plot points.
Factual errors
Danny searches for, and eventually finds, a pearl amongst his oysters from the restaurant. However, the edible oyster doesn't produce pearls, which come from an entirely different species of oyster.