The impeachment proceedings against Willie Stark take place in 1954, but as Jack Burden is walking up the steps of the capital building at the end of the film (the steps list all the states in the order they joined the union), you can clearly see Alaska and Hawaii listed. Alaska and Hawaii both became states in 1959.
Opening car scene at 3:27, looking at the speedometer, the steering column is visible with the keys and ignition switch on it. This is a replaced steering column from a newer car. Ignition switch on this vehicle should be on the dash. Steering column appears to be from an 80's General Motors vehicle, a common replacement for older vehicles such as this.
When Willie Stark is putting jam onto his crumpet, we get a close-up scene of him doing so while it is on the plate he is holding, in the next scene he is seen only holding the crumpet and then grabbing for a plate.
At the end of the movie when Adam and Stark fall on the Great Seal, Stark is clearly in the center of the seal and Adam on the edge with his arm and leg crossing the outside border of the seal. As the last shot pulls away they are both fully on the seal and Adam's arm and leg aren't even touching the outside border.
In the meeting at the pool hall, when Willie Stark first meets Mr. Duffy, Stark is introduced as the county treasurer of Mason City. The movie is set in Louisiana, which does not have counties. Therefore, he should have been called the parish treasurer. He is referred to properly by that title in the next scene in the newspaper office.
When Stark is giving the introduction to the new health facility/university, he is actually at what is called the Louisiana pentagon which is just left of the State Capitol building. The Pentagon is used as lodging for high profile out of parish state legislators and senators. The Pentagon was also the original site of LSU but the school was later moved to where its located now much earlier than the time the film takes part in.