A New Day in the Old Town - S2-E1
Visible crew/equipment: Lighting equipment is reflected on Nina's sunglasses when she tells Broyles to "save the day" after the Senate hearing. (00:31:40)
A New Day in the Old Town - S2-E1
Other mistake: The killer from another dimension shape shifts into the appearance of the victim, leaving the victim's body. But it transforms into Charlie's appearance and leaves behind its former female nurse shape, hiding Charlie's body to dispose of later. It would have needed to transform from the nurse shape, not out of nothing. The original nurse's body was not at that location.
Suggested correction: The shapeshifter transformed into Charlie using his dead body which it then disposes of at the end of the episode.
But when the shapeshifter transforms into Charlie, he shouldn't be leaving the body of the nurse behind since he had killed the nurse before entering the hospital and transformed there into her. The only dead body in that last scene should be Charlie's.
A New Day in the Old Town - S2-E1
Other mistake: Just after Olivia wakes up in hospital, she's trying to explain what happened, and we hear a heart monitor getting faster and faster - the doctor looks concerned and says they need to get her pulse down. But when we cut to the monitor itself it shows her heart rate as 72 - a perfectly normal value.
Night of Desirable Objects - S2-E2
Continuity mistake: Just before Walter's hand goes numb, Jean the cow can be seen alone in her pen. Then in the next shot, as Peter walks behind his father, Astrid has instantly appeared in the pen with Jean, brushing her. (00:13:40)
Night of Desirable Objects - S2-E2
Revealing mistake: When the typewriter is being used at the end, the keys being pressed don't correspond to the words appearing on the paper. Obvious from the start - the first letter pressed is on the middle row of the keyboard, but the first word typed is "unacceptable".
Night of Desirable Objects - S2-E2
Continuity mistake: A newspaper death notice of a mother and child is shown dated "September 1992". Two scenes later the tombstones of the same individuals are shown, dated "November, 1991"
Dream Logic - S2-E5
Factual error: When discussing whether Dr. Nayak's server could have been hacked, Agent Broyles says there was "no sign of a DDoS attack." A DDoS (Distributed Denial of Service) attack is not a means of hacking into a server to alter data - it refers to flooding a web site with so many connections, through automated means, that legitimate visitors can't connect to it. It's a mode of attack that has no relevance to the situation they were discussing.
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).
Character mistake: When Walter is saying his father was a scientific pioneer at the university of Berlin, Peter reacts by saying: "Yeah, I know. Who came here in 1933, which is long before the Nazi's ever took power." In fact it is EXACTLY when the Nazi's took power: 30 January 1933. (00:19:00)
Continuity mistake: Right at the very end, Olivia comes to meet Peter at his place for drinks. While Peter goes to grab his coat, her hair moves behind her right shoulder in a consecutive shot.
White Tulip - S2-E18
Factual error: Right before the cut to the title credits, the Via Rail Canada logo is visible on a train car, even though it is supposed to be taking place in Boston.
Visible crew/equipment: When Walter and Olivia leave the hospital in the alternate universe, William Bell pulls up in his vehicle. As he does, you can see the reflection of the crew on the metal bars in the front of the vehicle, as well as the metal side-view mirror.