Continuity: In the scene where Bartlet explains the Post Hoc fallacy the shot shows him taking off his glass, the following shot from behind has them on. The shot following and showing his face show the glasses off again.
Errors made by characters (possibly deliberate errors by the filmmakers): After Sam finds the call girl Laurie, she explains to him that she has broken some State laws, but claims to have never broken any federal laws. However in pilot she is shown in bed smoking marijuana which is a federal offense.