Saul stated that he was in room 312 but the room number on the door was 57.
If the series is set in the 1950's the pay phone is wrong. It would have a different handset and cord. Not the handset or the silver cord in the episode.
The $100 bill that Archie gives Orrie does not have Benjamin Franklin on it, and actually appears to have a woman's 3/4 profile.
While Archie is outlining his offer to sell information to Jean Estey, the shadow of a crew member can be seen through the doorway behind him, moving across the furniture in the next room.
Nero Wolfe keeps the uncashed $10,000 retainer check in order to earn the money, even though the woman who wrote the check was murdered. But an uncashed check written by a person who dies before the check is cashed is not negotiable. It is voided by the death.