Continuity problems over episodes are actually more understandable than the ones within episodes. The following is a beginning list of problems just within particular episodes.

In Six Meetings Before Lunch, C.J. tells POTUS that "you, me, Charlie and Zoey are the only four people who know she was lying." Yet C.J. told Sam about Zoey lying to the reporter, so there are FIVE people who know. (And most likely Gina as well although C.J. can't prove it.) This was pointed out to us by Jenny.

A Congresswoman is introducing a rider on an evening when the First Lady claims Congress is not in session. [#17]

In the first episode the staff was called about the President's bike accident around 5:30 or 6 am. "If everyone in getting paged about the sudden arboreal stop around six am - doesn't that mean that the 'stop' occurred around four am Jackson Hole time?" Cathi Soriano posted this question on the Television without Pity West Wing Forum. How much earlier could the accident have been? If it was during daylight that would have been a whole eight hours earlier than they were called. Surely they would have been called within four hours of the accident. So the President must have been riding around on a bike sometime after 11 pm and before 3:30 am. No wonder he ran into a tree since it was dark out there at that time. [#101]