Depending on whether you go by the timeline of the 1924 Broadway play, the 1927 silent movie, or whatever year the 1975 musical revival represents this film certainly takes place in the 1920s. Early in the film Mama Morton is heard mentioning going to Big Jim Colosimo's, a famous gangster of the era. Big Jim was murdered in 1920 and couldn't have been alive in the mid 1920s. Also 'bobbed hairstyles' were not a norm in the year 1920. Women would have still been wearing long hair as they had before WW1 in the Victorian and Edwardian eras.
Although Amos gives Flynn "large bill" currency notes (25% larger than the "small bills" in use since 1929) when paying Roxie's retainer, Velma and Roxie clearly use anachronistic small bills in the prison scenes.
At 1:28, Velma and Momma are listening to the trial on a radio. The tubes are visible, glowing white. Real tubes of that era glow with a soft orange light. If they were glowing white, they would last about an hour, if that.
In their final dance, Velma and Roxie are presented by someone who speaks on a microphone next to them. However, when the second part of their act is introduced, you can hear the same voice, but the man who was talking on the microphone has turned around looking at the musicians and the microphone is far away from his mouth.
Assistant District Attorney Harrison is referred to a number of times throughout the film. As charges of murder fall under State jurisdiction instead of Federal, "District Attorney" is inappropriate - rather, it should be "State's Attorney".
When Velma and Roxie are dancing in the final scene, they come out with the guns, and start dancing with them. They put the guns down on the stage and walk away to do a cartwheel. In the shot of their actual cartwheels, the guns are suddenly placed in a stand. But when they pick them up, the stands have disappeared.
During "Cell Block Tango",as Liz twirls and lands on her partner Bernie's knee, a lock of her long hair lands on top of his head. In alternating medium/closeup shots, the lock of hair disappears/reappears on top of Bernie's head.
During the scene "I can't do it alone" there is one shot where Velma cartwheels over the chair, and we can see Roxie looking straight at her. But in the very next shot, Roxie is looking down at a paper, and just giving Velma a small glance with one eye.
When Velma is in her dressing room getting ready to go onstage she opens her suitcase with clean hands. She rifles through it to get her gun which is wrapped in a bloody handkerchief, she then turns to a mirror and her hands are bloody as well much too bloody to have picked it up off the handkerchief. Also the blood did not wear off onto the faucet when she was washing her hands.
During the Roxie Hart song, right after she sings "who says murders not an art" Roxie walks past a line of mirrors. Halfway through the shot the camera crew is visible in the refection just to the right of Roxie.
Near the beginning of the song 'Razzle Dazzle', when Roxie and Billy walk up to the reporters' seating area, a reporter on the left can be seen reloading the flash bulb on his camera. When he lifts up the camera to take a photo, the bulb falls out, yet the flash still goes off.
The goof items below may give away important plot points.
Mama Morton tells Roxie that no woman has been hanged in Illinois in years. Later, Mary Sunshine tells her radio audience that Hunyak is the first woman ever executed by Illinois. In actuality, Illinois executed a woman in 1845 (three in total since 1938); Hunyak would have been the second.
At the end of the movie when Velma approaches Roxie with a job offer after her dismal nightclub audition, Roxie buttons her coat while preparing to leave. In her next speech the coat is swinging open, then is firmly buttoned again after she passes through the doorway.