When Hannah and Johnny take shelter from the rain in a shop door-way, they are pushed together twice by people exiting the store. The door begins to open a third time behind them, but the camera angle changes and no-one exits the store.
Most or all of the musical arrangements, costumes, and hairstyles date from a much later time period than the setting of the film (1912-1913). This is especially notable since many scenes are stage performances. Although a haphazard attempt is made to made the women's street clothing and hats vaguely appear at least near or approximate to the 1912 time frame, from the knees down, the light colored stockings, and most definitely all the shoe styles, are strictly 1948.
While Fred Astaire's slo-mo dance routine to "Steppin' Out with My Baby" is an impressive technological feat, he is seen performing it in a live stage show, where it would not be possible to do slow motion.
When Don sings the first line of "It Only Happens When I Dance With You" to Nadine, the shadow of the mic rises from the bottom left-hand corner of the painting above the mantelpiece and goes out of shot.
Robert Patrick says in his book, "Film Moi": "The most beautiful goof in movies comes in the 'Steppin' Out with My Baby' number. Fred Astaire at one point goes into slow motion. The chorus behind him continues at normal speed, but that's not the goof. Judy Garland, in the wings watching this miracle, just beams with admiration - as well she should."
In the "Roof Garden" scene, Nadine is wearing high heels when she does the "Magazine Cover" number. In the wings at the end of it, she removes her headdress, discards her huge fan, and goes back onstage to call Don Hewes out of the crowd to dance their old number. Suddenly, she's wearing ballet slippers. In fact, in all of her scenes with Don, she wears flat shoes, so as not to tower over him.
Watch Hannah's hat in the "Fella With the Umbrella" scene. She makes it through the drops to the umbrella with her feather relatively unharmed. The shot changes to a close up and her feather is drenched. Later its standing up straight again, then down again. Its pretty obvious that the close up shots were filmed before or after the longer shots.
When Hannah is going to play "It Only Happens When I Dance With You" on the piano, she opens up the music. Music is only on the right side, but in the next shot there is music on both sides and neither Don or Hannah turned the page.
When Hannah returns to her hotel after Don dances with Nadine, and finds Don waiting for her in the corridor....they are in the wrong set. The following scene shows Johnny arriving at her hotel room the next morning, and the corridor has a totally different decor: different door panel, door-lock, general colour-scheme, and with pictures now on the walls, etc. This set however ties in with earlier views of her hotel room.
In Mike's bar, a motto is shown with the possessive form of "its" spelled as "it's". While this is incorrect today, the possessive form was spelled this way up until the 1940s, and thus could well have been around in 1912.