Plot hole: In the pilot, it is established that the surface of anything/anyone made invisible by "quicksilver" is freezing. (Darien gets caught in the women's shower because the mist freezes on him. He freezes the beer mugs for the doctors.) But in later episodes, nobody notices him standing invisible - and freezing!? - next to them.
Continuity mistake: When Darien reaches into the glass spider enclosure to retrieve the note, the number of spiders sitting on the paper changes (too quickly for them to have crawled away and back naturally). First there are two on top of the paper, then only one, then instantly two again. (01:11:30)
Continuity mistake: The blood stains on Kevin's white lab coat change size and position several times between takes. (00:40:00)
Visible crew/equipment: When Darien opens the door and comes outside to meet Hobbes, the glass reflects the camera crew twice as it opens and then closes again. (00:07:40)
Continuity mistake: The assassin rips out a magazine page with Leila's photo on it and sets it ablaze with a cigarette lighter. The face in the picture burns while he's still holding the page. But in the next shot, after he drops it, the face is still intact and starts to burn all over again. (00:22:30)
Continuity mistake: A visible Darien leaves the sleep clinic in a downpour, getting soaked in the process. But when he climbs into the van to report to Hobbes, he's completely dry. (00:17:00)
Money for Nothing (1) - S1-E22
Continuity mistake: In Darien's apartment, the wall clock, which is running, reads 8:20. But his watch, which is also running, says it's 5:55. (00:21:45)
Visible crew/equipment: When the van races up to the hospital entrance and the door opens, it reflects a clear image of several film crew members, including the man holding the pole rigging for the boom mike. (00:18:20)
Continuity mistake: When Darien wakes up, following the RNA injection, with his brother's memories, his hair restyles itself several times between takes. (00:11:25)
Continuity mistake: The cut on Darien's forehead changes positions, then vanishes the same day, after he goes home to make the video tape. (00:24:20)
Factual error: Darien sets up a tripod and videotapes himself leaving a message for the Agency. When the tape is played back later, the camera can be seen to have both zoomed in and panned to follow his movements, even though no one was there to make those adjustments. (00:30:30)
Germ Theory - S2-E11
Continuity mistake: When Hobbes enters Claire's lab, the wall clock (which we can see is running) reads 9:15. Four minutes of continuous scene later, though, it's still 9:15 - and the clock is still running. (00:10:00)
Continuity mistake: The bullet holes in the side of Hobbes' van change positions, disappear and re-appear throughout the episode. (00:32:40)
Continuity mistake: Early in the first season it was established that Darien's parents died in an accident, and that he and his brother were raised by an aunt and uncle. But here, Darien's father is alive, is said to have "disappeared" years before, and there's no mention of the accident he "died" in.
The Three Phases of Claire - S2-E16
Visible crew/equipment: In the climactic fight aboard the shipyard scaffolding, Claire's stunt double is apparent - as well as obviously male. (00:35:00)
Continuity mistake: The establishing shot of the Agency's headquarters building zooms in on 3 tall, narrow windows recessed into a brick wall. We then cut to an interior view - of several wide, continuous windows without any recesses. They don't match the exterior windows at all. (00:07:30)
Visible crew/equipment: Hobbes opens the Agency van's door, and captures the reflection of a large round stage light. (00:18:20)
Continuity mistake: In the nuclear power plant, Darien picks up the technician's box of snacks, holding it by the narrow edge. Then the shot cuts, and he's instantly holding it with his hand spread across the wide front of the box instead. (00:35:30)