When we first meet the mirror T'Pol, she wears the rank insignia of full Commander. Then, in a subsequent scene with Archer, she has the rank of a Lieutenant Commander, but she was never shown as being demoted.
The Starfleet chest emblems used for the dead Defiant crew are wrong. The dead crew and later some members of Archer's crew are wearing TOS style uniforms but the emblems are not consistent with what had been worn in The Tholian Web (1968). In "The Tholian Web", the Defiant crew are wearing the traditional "delta" chest insignia. This is visible in several shots as Kirk and the team investigate the ship. Also, Gene Roddenberry and Robert H. Justman had a standing order and reinforced in a 1967 memo that all actors/Starship personnel "wear the Starship emblem that we have established for our Enterprise Crew Members to wear". This memo was posted on a Star Trek BBS.
When T'Pol and her Vulcan aides break in to the brig to free Captain Forrest, they throw a "flashbang" grenade into the room to disable the guards. Forrest is protected from the bang by the holding cell, but should still have been affected by the flash.
When Archer rises from the shared bed during a serious conversation, the piece of lingerie covering the left breast of Linda Park (Lt Hoshi Sato) almost becomes dislodged, and she slightly giggles as she uses one of her hands to keep it in place, before she becomes all serious again regarding the ongoing conversation.