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.
Continuity mistake: When Walter tells Peter that the Cocabeans he bought can't be eaten, he takes the roasting pan off the bunsen burner. In the next shot, the pan is still on the burner. (00:06:55)
Continuity mistake: After Fauxlivia shoots Joe and is dragging him to the bathroom to dispose of the body, she hears a knock on the door. During this shot, she is dragging him with his jacket over his head, which she is gripping. However in the immediate next shot, she is still dragging him by his jacket, only the jacket is much lower.
Other mistake: Peter and Dunham are alone in an apartment with blood coming in under the door. They are called and leave for the subway. Peter should have had to walk through blood to leave.
Continuity mistake: When Walter is using the hammer on the block of ice, the pattern that results is different when viewed from each side.
6:02 AM EST - S3-E20
Continuity mistake: This is after Olivia has bumped into Walter in the hallway. She gets back into bed and tells Peter that his father is walking around the house naked. Peter laughs and says it's normal for a Tuesday. The sun is on Peter's left cheek in shots from behind Olivia. In the reverse shots from behind him, the sun is missing. (00:07:30)
And Those We Left Behind - S4-E6
Continuity mistake: While beginning to take the radiation readings of the Jeep during his time jumps, Peter has a wedding ring on his finger. After cutting away and back again, the wedding ring is no longer on his finger. (00:15:15)
And Those We Left Behind - S4-E6
Plot hole: The very ending scene where Peter (in this version died in the ice as a boy so Walter's wife never met him) takes off some of the dust covers then picks up a toy airplane. The toy airplane he got as a child from ... Walter's wife when she was trying to placate him in an earlier episode for trying to run "home". This toy airplane wouldn't have been his as a child in this version of the universe. (00:42:00)
And Those We Left Behind - S4-E6
Factual error: In the final scene with Peter and Olivia in Walter's campus housing, Peter uncovers items that should have been in the house for years and they are dusty. The last thing he uncovers is a brand new flat screen HDTV with stickers on it, which would not have existed 17 years prior to then, when he was committed to St Clarie's Institution. (00:42:10)
Other mistake: In the scene where Peter and Lincoln are driving to question Daniel Hicks, a crew member is playing a practical joke that was somehow missed in editing. If you look at the left side of Lincoln's face, someone is hitting him with a laser pointer. This is definitely not part of the script (i.e. Sniper rifle scope), as no one is actively targeting members of Fringe in this part of the show. (00:16:20)
Brave New World: Part 1 - S4-E21
Continuity mistake: This is when Peter and Olivia are discussing different Boston's suburbs as their potential new home. The sun is on the right side of Olivia's face in one shot. In other shots, it isn't.
Answer: He helped his father evade capture, impeding the investigation.