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.
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".
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.
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.
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.