Continuity: 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.
Factual errors: The New York Blizzard that Gilda sings of, actually happened two years later in 1888.
Errors in geography: At the airport scene, you can see hills in the background. In fact, the Buenos Aires' area is totally flat.
Revealing mistakes: The sign says "LIBRETAS DE ENROLAMIETO". The correct spelling is "ENROLAMIENTO".