Revealing mistake: Any time any character is driving a Suburban, or any other vehicle with a column mounted shift lever, the shifter is in park while they appear to be driving.
Continuity mistake: Charlie, Olivia's former partner and friend in the FBI shows up in this episode during the interview with Mrs. Rusk, but Charlie was killed off by one of the shapeshifters in a previous episode, and the shapeshifter that killed Charlie was himself killed off by Olivia, who in other episodes reflected back on killing him. This episode was supposedly meant to be in season 1 as ep 21 or 22. Unknown why they didn't air it then, and decided to put it in the middle of season 2 (for no apparent reason).
Continuity mistake: All shots of the Jeep Cherokee prior to it crashing (and during the process of flipping over) show that it wears factory-optional silver steel wheels of a 'star' style. But as the wreck settles upside-down, it's wearing plain steel wheels (like those found under full wheel covers or on a spare tire).
Plot hole: Parker gains access to the external room using a valid security card, they figure out the CEO's passcode which opens the burn room door...and yet the room inside is still protected by a swarm of lasers. Was the CEO supposed to dance through the laser sensors like Parker does every time he goes in?
A Knight In Shining Armor - S1-E1
Continuity mistake: When Kitt's on fire, before getting back to the HQ, we see a shot of the main HQ screen, and towards the bottom left is a screen with a picture of Kitt and green writing reading "Fire extinguished".
Audio problem: They went to an investigator to let him listen to the audio. The audio with the woman screaming and the gasp, the gasp was Zak, not another apparition.
Continuity mistake: When Mary talks to Bobby D at the crime scene, her hair moves back and forth over her left shoulder between shots throughout their conversation.
Containment - S1-E5
Continuity mistake: At the end of the episode, when the bad guy is preparing the syringe of small pox, he follows the usual method of tapping out any air in the tube - when he is shown injecting himself, a large air bubble is back in the syringe (which would probably kill him quicker than the smallpox).