Factual error: Scarlett is seen walking on the main street on the way to the hospital. You can clearly see a light bulb in one of the street lights. (01:05:25)
Factual error: The filibuster scene gives the impression that the Senators were powerless to stop Jefferson Smith's speech. However, they can make a speaker shut up if at least 3/5 of the Senators vote to. From the Senators' reactions, a lot of them probably would have voted to silence Smith. (Clearly, if this had happened, the movie would be much less interesting).
Factual error: The distance from Lee's Ferry to Lordsburg is over 500 miles, not a trivial distance by stage coach. But in fact, the stagecoach travels several times through Monument Valley, back and forth. Monument Valley is on Navajo Reservation, nowhere near the Apaches or Geronimo.
Factual error: Towards the beginning of the film, when Kitchener is shown inspecting Harry's old regiment, one of the African or Egyptian troops is shown to be wearing the Pattern 1914 Infantry Equipment, not made until 1914 at the earliest. Additionally, it has the 1918 modification to have two closing straps, so is over 20 years too late for the 1894 date at that point.