When they are brought to a corner of the crowded night club, they are sitting at a round table. Next to them is a round table that has a burning candle stick. A girl is being swung around over them, blowing out the candle. When the 6 actors decide to get up and join them the candle which had previously been burned out is now lit and has a hurricane glass over it.
When the cops are chasing the cab through Manhattan and across the Brooklyn Bridge, the sky is at twilight, even though it's supposed to be shortly after midnight.
The tall metal "suicide fence" on the 86th floor of the Empire State Building was installed in 1947; however, when the characters visit the observation deck in 1949, there is no fence.
In the opening song sequence the men leave Brooklyn Naval Shipyard at 6 am, walk across the Brooklyn bridge, travel to Wall St, Little Italy, Chinatown, the Statue of Liberty, Washington Square Park, Lower East Side, Grant's Tomb, Riverside Church, Central Park (where they rent both bikes and horses), take a bus tour and go to the Observation deck of Rockefeller Center and end at 9:30 am. This would be physically impossible, the boat trip to the Statue of Liberty alone would take 3 hours.
When the dinosaur skeleton collapses, the head goes up instead of falling.
When the characters arrive at the Museum of Anthropological History, a tour guide claims that the dinosaur shown onscreen roamed the world 6 million years ago. Dinosaurs went extinct 65 million years ago but this was not known in 1949.
On the drive to Coney Island, the cab pulls inside a fruit stand and one of the sailors grabs a sign to hide behind. The background music that plays is "Shave and a haircut, two bits" but the sign reads "Shave and haircut 75 cents." Two bits is actually only 25 cents. However, the song is also well known with the price of "six bits" (75 cents), and either way, no words are sung.
The cab is a 1947 DeSoto, but the cutaway used for the interior shots is obviously a much earlier, pre-WWII model, the shape of the windows, particularly the rear windows, being noticeably different.
When the boys dance on a bench atop the Empire State Building, the blinds on the other side of the wall wobble as they move, revealing the wall is really a set.
None of the sailors salute the flag as they board/leave the ship.
Right before the "You're Awful" number, Chip (Frank Sinatra) throws the guidebook off the top of the Empire State Building. However, the sound of the guidebook landing on the ground can be heard, suggesting that the scene was shot on a set.
At the 16:50 point in the film, Ozzie knocks on the window between the driver and the back seat, breaking it. No one acknowledges the broken window. The actors ignore it and continue to act through the scene as if he didn't break the glass.
Chip's guidebook is said to be from 1905. Yet, it includes the Woolworth Tower and the Cloisters. Construction on the Woolworth Tower started in November 1910 (concluding in 1912). The Cloisters, a museum of medieval art, was established in 1938. (In the stage version of "On the Town" Chip's guidebook comes from 1934, but its mentioning the Cloisters is still an anachronism.)
In the dance studio when Gaby tells Ivy what time to meet him, they both mouth "seven-thirty", but a voice overdub corrects both to "eight-thirty", which is the time Gaby set with the rest of the group.
Spectators can be seen watching the filming of the "New York, New York" number in Rockfeller Center (though it could be argued that the sight of three men in navy uniforms singing and dancing might attract attention, even in New York).
Near the end of "Prehistoric Man" when the dancing moves in front of the dinosaur, Claire's mark can be seen on the floor.
When the boys are looking for clues on the poster in order to find Miss Turnstiles, they find her likes and dislikes. However, none of that is actually mentioned on the poster they have or any that the viewer sees.
At approx. 6 mins, in the lyrics of a verse added to "New York, New York" for the film, Ozzie (Jules Munshin) sings (presumably referring to himself, Chip and Gabey), "We've sailed the seas and we've been the world over, / From Maine to Mandalay, / We've seen the Sphinx and seen the Cliffs of Dover..." However, at approx. 7 mins, Chip (Frank Sinatra) says, "I never been anyplace but Peoria."
Near the end of "Come Up To My Place" Sinatra rolls up the window of the cab and catches a lock of his hair in the window. Without missing a beat in the song or his character's actions he opens the window enough to free his hair and continues the rest of the scene flawlessly.