Corrected entry: In the first season, every employee in the west wing (except the president) is wearing an ID badge. Since then, only a few people are seen wearing them, but surely the policy of the White House hasn't changed since then?
Evidence of Things Not Seen - S4-E20
Corrected entry: When CJ Cregg is balancing the egg in the final scene, the clock on the wall says midnight, which in the show it is, but her wristwatch shows 7.20.
Correction: Wristwatch batteries go dead and people forget to wind watches, too.
Holy Night - S4-E11
Corrected entry: Toby's father is mentioned as having worked for Murder, Inc; however, the opening scene with him on assignment is set in 1954, while Murder, Inc ceased operations in the mid-forties.
Correction: Murder, Inc. was simply a joke referencing Toby's father's past in the mob business. I really, really doubt that this was a real reference.
There's nothing in the scene to indicate that it was a joke, and the flashback is - apart from the anachronism - reflective of the actual organisation's operations.
Correction: After a while, the guards and Secret Service would come to recognize the "big players" - Leo, Josh, Toby. They wouldn't be required to wear their badges, although others might be.