In long shot, the milk truck is a 1937-1939 Stutz Pak-Age-Kar. No paint stripes down the hood, no large name badge, square front windscreens, twin bright bumper guards. When it arrives, it's a 1939-1942 White Horse van, with heavy bumper over-riders, slanted windscreens, large badge and lettering on the front. Vehicles are mixed through rest of scenes involving milk trucks.
As Joe and Alice walk through the museum, Joe isn't carrying their bags but there was no scene of them storing them somewhere during their visit.
When Alice's roommate changes clothes, she partly removes her blouse but then re-buttons it before finally changing tops.
Joe shows up for his date with Alice at 7 pm. And even though their date lasts nearly a day, he's still clean-shaven 24 hours later.
In the opening scene when Joe walks across Penn Station and approaches the man with the matches, the actors mark is clearly visible on the floor.
The escalators in the train terminal are obviously just rubber conveyor belts, and the handrails are not moving.
When Joe stops running after the bus Alice is on, the pavement on the rear projection screen behind him keeps moving for a few seconds.
When they get separated, Joe is running alongside the train departing on the tracks. The next shot that shows the back of the train heading into the tunnel might have been reversed for some production reason because there is a sign on the wall with what appears to be a backwards six (6). Also when looking in the back windows of the end car, there seems to be nobody or very few people in it. But, when she was pushed into it, they were packed in standing room only.
The film was released in May 1945; at one point, Judy asks Robert Walker (referring to the guard at the blood test building) "Who does he think he is, Hitler?" Hitler was already dead when the film was released.
Although the film was released in May 1945, production was completed in November 1944 - before Hitler's death in April 1945.
As they're riding up Fifth Avenue on the bus, she points out Radio City and St. Patrick's Cathedral. Radio City isn't on Fifth Avenue, it's on Sixth Avenue. A moment or so later, as the continue riding up Fifth Avenue, the statue of Atlas at Rockefeller Center is seen in the rear projection background. The statue is directly across from the cathedral, which they should've passed already.
When Robert Walker is headed back down the escalator to get the heel of the shoe, you can see Judy Garland look up either for direction or for a cue as she is sitting on the post next to the up escalator.