Long Live Walter Jameson - S1-E24
Factual error: When Walter is reading the diary of the Civil War soldier at the beginning of the program, he reads an entry from "Tuesday, September 11, 1864." Tuesday, September 11, 1864 was a Sunday.
Continuity mistake: When Cadwallader puts a seal on the Escape Clause paper, he presses so hard that he manages to lift the whole document with seal. You can see that there is absolutely nothing except for a seal mark on the paper, yet when he drops the paper to the floor some typed text appears on it. Also in the same scene, the seal pattern is square in the first shot, but when the paper drops to the floor the seal mark is round.