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.