When Johnny is beaten up by Mundson's henchmen, his tie jumps out of his coat. Later, when he is talking to Mundson, his tie appears untidily held by his coat.
When Farrell asks to cut the deck at the blackjack table, he shuffles the deck prior to the cut; this is not allowed.
When Johnny is in the casino watching the roulette game, the ball is circling the inside of the wheel, but the wheel itself is standing still. A roulette wheel never stops moving while the table is open.
When Gilda plays the guitar, her fingers don't move according to the tune.
The sign says "LIBRETAS DE ENROLAMIETO". The correct spelling is "ENROLAMIENTO".
Gilda tosses her acoustic guitar at Johnny and hits the glass decorative divider, instantly smashing it. However, this would not happen with a lightweight guitar like that. Perhaps a solid wood electric guitar would break it, but the glass divider would be a minimum of a 1/4" thick, and even then that would be too flimsy for a real divider in a nightclub. The guitar would suffer the brunt of the damage, not the divider.
The men's room in the casino has no sign on the door or any other marking indicating that it is such. The standard round door knob, which few if any restrooms have, further disguises its purpose. Particularly in a building populated by so many wealthy international customers, the restrooms would be clearly identified. It looks like a storage closet.
At the airport, hills can be seen in the background. In fact, the Buenos Aires area is totally flat.
The New York Blizzard happened in 1888, not 1886 as Gilda sings.