In the Cub room, after Eve has returned from her restroom talk with Karen, Addison DeWitt is tapping his cigarette into the ashtray. The cigarette falls off from the holder. He continues tapping until he realizes it fell off and then he attempts to hide the holder behind his hands.
When Eve tells her life story in the dressing room, she says "then the war came, and we got married. Eddie was in the air force - and they sent him to the South Pacific." The Air Force, wasn't formed until after the war in 1947. During the war it was called the Army Air Forces.
At the beginning of Addison DeWitt's "introduction-speech" of everyone in the movie, he's supposed to look at the stage, but the rest of the audience behind him is clearly staring in a different direction.
About 45 minutes into the film, Margo and Bill are having an argument about Eve before his birthday party. Margo angrily folds her arms across her chest and her diamond bracelet clasp breaks and dangles against her dress. It isn't part of the story. It is fixed in the next frame.
At right about 51:58 into the movie, when Margo and Lloyd are talking in the kitchen, right after Margo says "Cora...still a girl of twenty", the camera that is filming the scene shakes as if it was accidentally bumped.
When Addison and Eve are together in the Cub Room, he taps his cigarette holder to knock the ash off the cigarette, which falls out of the holder into the ashtray. He doesn't notice while he speaks, and keeps tapping the empty holder.
When Karen, Bill and Margo are returning from a long weekend in the country, they run out of gas. They mention having driven the car over the last few days, but in the two closeups of the dashboard the odometer only reads between 00023 and 00024 miles - the studio probably bought a new car and cut it apart for the interior process shots.
When Eve and Addison De Witt are walking down the street in New Haven from the Schubert Theater, the pedestrians behind them are walking at a faster pace, but never gain any ground on them. This is because "back projection" is being used; George Sanders and Anne Baxter are not really walking down a street. They are "walking in place" and the background is actually projected film being shown behind them.