Revealing mistakes: When Smith arrives in Washington on the train, he's seen walking towards the exit with a porter behind him carrying his bags. The next shot shows the same porter coming into the station carrying someone else's bags.
Continuity: When the governor enters the Smith's home (with the band playing) we see, from the outside, Ma closing the door almost shut. When the scene shifts to inside the house, Ma is again closing the same door.
Errors made by characters (possibly deliberate errors by the filmmakers): When Senator Paine snaps at the end, he refers to Jim Taylor as "Willie Taylor". Since Kapra was under extreme budget controls it was deemed too expensive to re-shoot the scene. Most people never notice.
Errors made by characters (possibly deliberate errors by the filmmakers): Jefferson Smith refers to "that lady that's up on top of this Capitol dome, that lady that stands for liberty." Actually, it is the Statue of Freedom.