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 Declaration of Independence shows the "S"s are written in modern style script and not the "F"s style as in the original document.
Suggested correction: The document shown is a correct reproduction of the Declaration of Independence and is identical to the William Stone version (identical to original though cleaned up). In the original lower case S's were written in an 'f' style (indiscernible in the movie), but the capital S's in the title are how they were written. It should be noted though that the close up version shown in the movie is not the document actually on display at the National Archives since the creases and ink marks are absent and the text isn't badly faded.