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.
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.
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)