When the little girl is on Santa's lap, the white gloves she is wearing disappear from her hands as the shot changes.
Errors in geography
As Ralphie walks down the streets of Hohman, Indiana, a New York City subway entrance, complete with a modern graffiti tag, is visible.
The Buick Roadmaster is said to have a two-speed Hydra-Matic transmission. Hydra-Matic transmissions were never two-speeds (in the '40s they were four-speeds). Buicks were known for having DynaFlow transmissions, not Hydra-Matics, and the DynaFlow was not available until 1948.
The used Oldsmobile Ralphie and his dad look at is a 1941 model. The salesman says it is an Olds 88. The Olds 88 wasn't introduced until 1949.
The hole The Old Man drills hole in the ice is too small for a small fish to pass through, never mind a larger one that would have fed his entire family.
On Christmas Eve, 1946, Ralphie passes a theater with It's a Wonderful Life (1946) on the marquee. The film was released on January 7, 1947.
Black students are at Ralphie's school in 1946. Indiana schools were not integrated until 1949.
The invoice in Higbee's is dated 1946, but one of the side stories features Franklin D. Roosevelt, who died in 1945.