Character mistake: Previous episodes have established this story arc to be occurring in the year 2154. Yet here, when T'Pol records her log, she cites the date as 2152. (00:32:00)
Factual error: At the very end of the episode after Loomis is arrested, the camera pans away from the Detroit street, but mountains can be seen in the background on the horizon. There aren't any mountains or even large hills near Detroit.
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.
Revealing mistake: While Archer and the crew discuss the capabilities of The Xindi vortex technology and whether or not to go to Azati Prime, Archer asks Trip to see the data that Trip has collected from the Degra's ship. The camera pans to the display screen, on which a Mac mouse pointer is visible. It is positioned on the line going downward from the red giant.
Continuity mistake: At 38:20, T'Pol (as acting captain) says that they have resumed their course to Azati Prime; however, from 39-42 minutes, Captain Archer and Trip discuss the "current" status - that they are still orbiting the planet and then the Captain orders Trip to tell Travis to set a course for Azati Prime at maximum warp. (00:38:20)
Continuity mistake: The captain's log date of Jan. 8, 2154, doesn't align with the timeline of previous episodes. Harbinger, two episodes earlier, was said to take place Dec. 27. The episode in between that and Hatchery, Doctor's Orders, wasn't given an on screen date, but T'Pol compared the anomaly in that episode to the one in Harbinger, which she said was encountered a few weeks earlier. Even if that was just two weeks earlier, that would put Doctor's Orders at Jan. 10, and that episode spanned at least four days, so the earliest Hatchery could take place would be Jan. 15.
Continuity mistake: When Hayes takes off his jacket before sparring with Reed, he tosses it to his right so that it's on the right side of the room. When he picks it up, it's now against the wall that's on the left side of the room.
Suggested correction: When he takes his jacket off his right arm is the last to come out and even though you can't see the jacket anymore you can see his right arm go across his body like he is throwing something to the left.
Continuity mistake: When The Xindi weapon first jumps out of warp and approaches Earth, its flies straight towards west Africa, however moments later as it fires its weapon it's east of Newfoundland.