Visible crew/equipment: In the opening shot, as the camera moves down the building, in the windows you can clearly see the cameraman & camera on the hoist/crane. (00:01:00)
Visible crew/equipment: In the second before last scene (when John and Kate finally met and are hugging each other in the center of the ice rink), the camera moves around them in a loop and at one point in the background, we can see the snow being shot out of the snow-making machine located just outside the rink. (01:24:05)
Answer: It is not a movie mistake. The scenes were filmed at the Trump Skating Rink (formerly called the Wollman Rink) in New York City's Central Park. The arena has traditionally been used for multiple venues throughout the year including ice skating, roller skating, concerts, carnivals, etc.
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