Continuity mistake: In the opening scene, Tom stands outside the General Store, and walks into it, through a door that is already open. However, in the next shot, from inside the store, both shop doors are still closed and Tom has to open them.
Visible crew/equipment: When Tom is ringing the pager number from the phone box, you can see office workers watching the filming of the scene from an upstairs window.
Character mistake: The voice tells Tom that the alarm deactivation code is 47223. However, when Tom enters the code subsequently to deactivate the alarm, he only enters "4723." You can tell he doesn't enter a fifth digit because the keypad chimes each time a digit is entered.
Factual error: Tom's mother lives in Iowa, but the flowers/plants in her garden include types that could only live in places with warm/temperate weather all year round - which is decidedly now the case for Iowa.
Stay Tuned - S1-E17
Factual error: The episode is set in New York State, but at the end the road signs are all for Oregon locations.
Factual error: Tom finds a notecard with an "internet access code" that is an IP address: 271.287.291.31. The problem with this is that IP addresses cannot go above 255 as the starting three digits - it's a completely invalid address.
Continuity mistake: When Tom gets a copy of his hospital admission records, his SSN is stated to be 542-68-4360. However, in an earlier episode ("A Rough Whimper of Insanity"), he tells the hacker that his SSN is 549-24-1889.
Through a Lens Darkly - S1-E20
Continuity mistake: At the end of the episode, Tom is absolutely drenched because the car has crashed into a river, and he has to wade through the river to get to the riverbank. However, as he walks away, he doesn't leave a single wet or muddy footprint behind him despite this.
Plot hole: Tom discovers Claire's body in the wardrobe of his motel room. He leaves the room, and within a minute returns to the room, accompanied by the police. The body has vanished from the wardrobe, but given how little time Tom was away from the room, it is impossible for someone to have moved it, particularly given the weight of a corpse.
Factual error: Enlisted soldiers are shown saluting each other, as well as addressing a sergeant as "sir." Enlisted personnel in real life never salute each other, nor are NCOs (like sergeants) ever addressed as "sir."
Stay Tuned - S1-E17
Continuity mistake: When Tom and the English teacher walk into the campaign HQ, a shot is shown of a security guard glancing up the stairs, and a blonde woman carrying a poster walking past. After Tom and the teacher have finished having a conversation with a balding man wearing glasses, the exact same shot is shown again.
Other mistake: When Tom looks at Sylvia's medical records, it states that she died in December 1994, but underneath that it states that she had bloodwork, eye tests and tissue examinations done in July and August of 1995.
It's Not Such a Wonderful Life - S1-E12
Continuity mistake: In the previous episode, Tom was shot and had a scar from the resulting bullet wound. In this episode, when he takes his shirt off on Christmas Eve while talking to Alison, the scar tissue has completely vanished. Bullet wound scar tissue - even after years - doesn't completely vanish. It's been less than months since the previous episode.
Continuity mistake: When Tom and the girl get back from the dance, they go into the sitting room to see that there is a roaring fire already going, with the stove door open and a whole log on the fire that's barely been touched. The fire is too high and the log too untouched to have been burning before Tom and the girl left to go to the dance, and there's no one else in the house to have started it before Tom and the girl arrive home and open the door to the sitting room.
Paradise on Your Doorstep - S1-E5
Factual error: The plane Tom hijacks is a Grumman Goose. This has a maximum altitude of around 20,000 ft. When the pilot flips the pressurisation switch, the instrument panel shows the plane is only at 2500 feet! The cabin wouldn't have depressurised at such a low altitude - and even had it done so if the plane had been flying much higher, it wouldn't have had such a severe and debilitating effect so quickly on Tom as suggested in the episode - he passes out in about 3 seconds.
Factual error: At the end of the episode, Tom is at a crossroads, theoretically in Iowa. However, the desert/scrub/mountain surroundings are scenery not found anywhere in Iowa.
Through a Lens Darkly - S1-E20
Continuity mistake: When Tom lifts up the girl's sweater (with both hands), he is still wearing his shirt. In the very next shot, he has magically lost his shirt too, even though his hands aren't free to take it off, and the girl wouldn't have had time to do so in the space of 1 second.
Factual error: A number of the soldiers on the US Army base have haircuts/hairstyles completely against army rules and regulations. This is particularly noticeable given the show is set in the late 90s, when the US Army was much stricter about haircut rules for serving military members. In real life, they wouldn't be allowed to have those hairstyles.
Other mistake: When Tom is sitting in the chair reading Ellen Combs' medical/surveillance file, the page he is reading just contains the lyrics from the Ella Fitzgerald song "Someone to Watch Over Me".
Factual error: When Tom is locked up in an institution for the mentally ill, he is given a bed on a mixed gender ward/wing (both men and women). Wings and wards in mental institutions have not been mixed gender for more than 100 years - it is inconceivable that this practice would be existing in the 1990s in a large city in the USA.
