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.
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.
Continuity mistake: At the very end of the episode when Nina Sharp exits the elevator, she mostly steps out of the elevator completely before the masked men come and shoot her. However, when they review the security footage of the attack in the next episode, "There's More than One of Everything," you see that she barely takes a step before being shot.
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".
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.
Plot hole: When interrogating Boone, Olivia shows him a photo of a body with the spine torn out in the woods. This body hasn't been found yet, as a later scene has Olivia and Peter go to the same location and find the body. You can tell it's the same body because the shirt is the same in both the picture and the crime scene.
Continuity mistake: This episode takes place over one day. It's Olivia's birthday at the start of the episode, and at night, she gets the card from her stepfather, implying that it's still the same day. Right before Broyles yells at Olivia in the Harvard halls, there is an establishing shot of Harvard where it is nighttime outside, but inside the building, there's sunlight coming through the windows.