Visible crew/equipment: In the episode, "Anomaly," at the beginning, when Phlox is looking at his animal cages, you can see a string or wire attached to one of them, presumably the means by which the cages are shaking.
Visible crew/equipment: As Travis struggles to hold up a piece of debris, a hand becomes visible from behind the data security bank panel for a few seconds before disappearing. (00:10:15)
Other mistake: Two Borg are discovered North of the Arctic Circle. One is covered in ice, the other encased in ice. Carbon dating shows the wreckage to be over 100 years old (to tie it in with Star Trek: First Contact). The Borg are inactive and unable to repair themselves until they are "defrosted". The temperature above the Arctic Circle doesn't usually drop below -100°F. The Borg have been shown to work very well in the vacuum of space which is 3-4K (roughly -454°F). If they can survive that, even being frozen in a solid block of ice would not slow them down. The nanites have to be in their "blood" and operate at the cellular level. That cannot be damaged by re-entry and the crash.
Commander Dolum: You don't want to know my specialty.
Captain Archer: Let me guess... stinking up the room?
Trivia: Season 3 of Enterprise is the only season of any Star Trek series to date in which no Klingons appear.
Question: Is the captain's dog still alive?
Answer: Yes. Porthos survives this episode, although many a viewers' sanity and the show's ratings were not so lucky.