Deliberate "mistake": 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.).

Continuity: In the scene where Jefferson Smith goes to talk to Senator Paine he fumbles with his hat when he meets Susan. As he bumps into the table on his way out his hat disappears.