When Peter makes breakfast, he has toast and scrambled eggs made into a sandwich. In the reverse shot, the pieces of toast are placed flat on the plate with the eggs on top.
When Dunham (in Walter's tale) goes into Rachel's apartment to find Rachel dead, her right eye is open/closed between shots.
During the noir scenes, Olivia calls Broyles "Lieutenant Broyles" when she meets him. In the next scene however, also a noir scene, Nina Sharp refers to him as "Detective Broyles", his rank in the show's reality.
When Peter and Olivia go to see Walter in the lab, the matchstick in Peter's mouth switches from left to right and back again between shots.
Walter is shown making a label for a calcium hydroxide solution and placing it on a bottle containing liquid. Calcium hydroxide is not soluble in water, so he can't have a solution of calcium hydroxide.
During one scene where Olivia visits Nina, there is a Windows logo on the back of a flat screen monitor. The time period this episode often portrays would have been before Windows existed. However, this is all part of Walters "noir" story, where characters also use mobile communication devices.