After getting off the train where he met Rosalind van Hoorn, Walter runs into her sitting in a yellow and red Skyview cab. He gets in with her. When he gets out the cab, it has changed to a pink and tan A&R Service Co. cab.
Rosalind puts her dress back on after it has dried from the rain. She then buttons it up completely, but the camera pans away and back, and she is buttoning the top button again.
When Rosalind van Hoorn goes into the library, she puts her handbag on the piano along with her fur coat. At this time she is wearing green gloves. She turns around and in the next shot she is no longer wearing the gloves.
When Walter realizes he left his briefcase in Rosalind's cab he hails another cab to go follow her. The cab he gets into is a DeSoto Suburban and has standard headlamps. When he arrives at the destination he arrives in a DeSoto Suburban which has hidden headlights.
The swastikas shown on the Spitfire are originally shown in reverse. Shortly thereafter they are shown the correct way round. Clearly the studio mocked up one side of a Spitfire and simply reversed the filmed image to 'show' both sides of the plane.
Walter Mitty's narration as an RAF pilot during the aerial dogfight with the Luftwaffe pilot gives his rank as Wing Commander. But during the subsequent scene in the cafe, he is referred to as Group Captain.
Reginald Denny wears an Air Vice Marshal's uniform in the RAF daydream, yet he is credited with playing the "Colonel". (Danny Kaye wears Group Captain rank insignia in the sequence, and is correctly called that by the other pilots.)
Tubby Wadsworth's prank spreads white powder on much of Walter's jacket, yet seconds later there is no trace of it.
When Mitty exits the office having just knocked over the water cooler, the glass in the door breaks. Just prior to it breaking you can see large scratches where the glass had been prepared for breaking.
The hidden museum items in the black book are all written down in English. Since the museum was in Holland, they should have been written in Dutch.