Kitty Collins ditches her brooch into a plate of soup, Rigby opens the brooch and pulls out a paper, which would be soaking wet but is clearly bone dry.
Field Marshal Von Kluck's (Carl Reiner) collar insignia are on the the wrong way. The right tab should should be on the left side and the left on the right.
In the grocery store by the boxes of Farina, in the shot with Steve Martin, the baby on the box is facing the left of the box. In the shot from Double Indemnity (1944) with Fred MacMurray, the baby is facing the right side of the box.
When Rigby is sitting in a chair with a drink while talking with Huberman (Ingrid Bergman)the film was reversed during editing resulting in Rigby appearing as a mirror image. Specifically, holding the glass in his right hand with his breast pocket and pocket square appearing on the right hand side of his suit, instead of the correct, left side. Between cuts, the image reverts to normal.
When Rigby is talking on Juliet's phone to her sister Leona, the handset and coiled cord to the phone are from the 1960's-80's, and not the straight cloth-covered phone cords in use in the 1940's when the story is taking place.
After drinking the "Mickey", Rigby is in the bathroom to shave his tongue. The electrical outlet next to the sink is a modern grounded (3 prong) model that wasn't in use until many years after the movie's 1946 time period.
At one point Reardon references the Kinsey Report; the first volume was published in 1948, but the movie is set in 1946.
The newspaper in the opening scene has a large headline saying "Dodgers Lose Again." But that wouldn't have been a big deal for a Los Angeles paper in the 1940s -- the Dodgers didn't move there from Brooklyn until 1958.
Rolodex card file wasn't marketed until 1958, yet appears on a desk in scene set in Forties.