Factual error: A number of times throughout the season they refer to LSD being found in dead bodies and LSD being matched with other LSD found in other (living or dead) bodies. LSD starts a chain reaction in the brain which requires about an hour to take a noticeable effect. And, by that time, it has completely broken down and no longer exists as LSD in the body - before the person even begins to get high. There is no test for LSD even in the most bombed living individual, let alone a dead body years later.
Sea Change - S3-E1
Factual error: President Dalton's memorial US Flag in his office is folded wrong and displayed upside down in the flag triangle. The US Flag is always displayed with the stars pointing up. (00:47:00)
Factual error: Constantine's driving licence is shown - it's a UK licence, but no. 7 where his signature should be is blank, and no. 8 where his full address should be simply says "England, United Kingdom." Both are printed onto the licence when it's issued - without that info it would never be issued in the first place. And it's not a fake, because why would he have a fake licence with his real information on it? It's just an incomplete prop.
Factual error: Congressman Tate and his brother are on the shooting range. They are wearing high-tech electronic earmuffs that block harmful noise like gunfire while amplifying speech and other low-volume sounds. Although, they are wearing high-tech earmuffs, they both have an ear exposed so they can hear each other talk. (00:13:00)
The Alchemy Murder Case File 3 - S1-E8
Factual error: The Latin text on the supposedly old tome (which is written with a modern font) displays an alchemist diagram. It is a reproduction of a famous drawing meant to portray the Philosopher Stone in the Sylva Philosophorum, but whoever copied it does not know Latin, because certain words are misspelled ("Merceralia" instead of "Mercurialia", "Humides" instead of "Humidus"). (00:10:10)
Factual error: The only person ever addressed as "Sir" is the brigadier, and then only occasionally. No other officers ever seem to be addressed in this way.
Episode One - S1-E1
Factual error: In the fairground chase the characters jump over some Heras fencing that wasn't invented until the next decade.
Factual error: Helmuth von Moltke is addressed and referred to several times as Field Marshal. He wasn't promoted to that rank until 1871. He was a lieutenant-general during the Second Schleswig War in 1864.
You Always Hurt the One You Love - S1-E1
Factual error: In the opening sequence, Dr Frank Winter is hitting golf balls in the desert while a radio announcer is reading off names of Americans killed in action. One name is identified by the rank of "Lance Corporal," which the US Marine Corps first adopted in 1958, long after the war. Several minutes later, Dr Winter dresses down an Army MP, referring to him as "Sergeant First Class." During WW2, that rank was actually "Technical Sergeant."