During the scene that Wayne Weinsider uses the baby monitor to eavesdrop on Mulder's phone conversation with Scully, Wayne is able to hear both Mulder and Scully's voices. In reality, the monitor would only be able to pick up Mulder's side of the conversation, Scully's voice over the phone would be inaudible.
At around 6:10 agent Jeffrey Spender has a sheet of paper in his hands given to him by a police officer. He tells him that he will make it a priority. When the policeman leaves he puts it in a shredder. Later Mulder retrieves it from the trash and puts it back together, this would realistically take considerable time if it were even possible.
Toward the end of the episode Betsy almost gets into a car crash with Mulder and Scully, and reveals herself to be covered with blood and no longer pregnant, saying that Wayne stole her baby. It appears she stops the FBI agents deliberately, but how did she know who they were? She never met either of them during the course of the story, and in fact there was no reason why she would even have known of their existence or that there was an investigation of Wayne going on.
Mulder tells Scully he is not a psychologist, even though he graduated cum laude in psychology from Oxford University.
At around 38 minutes, Mulder and Scully driving at night come across Betsy driving the red Camaro. Betsy gets out of the car, blood all over her, yet neither Scully or Mulder calls quickly for an ambulance.