Gortimer vs. The Mobile of Misfortune - S1-E3
Visible crew/equipment: When Stanley is riding the kart in the race, the shadow of the camera equipment is briefly visible bottom right, just before the kart starts to fall apart.
Continuity mistake: When Elizabeth starts weeping, her bodysuit is torn above her left breast with a single tear. Post-credits Meliodas asks her to join him; now that torn spot is split in two - the first time the bit of fabric that separates the two spaces was already severed. (00:17:40 - 00:22:30)
Continuity mistake: In the scene where Debbie clears everything off the mantle, she leaves the bronze baby shoes and turns to talk to Marty. Then we see over her shoulder that the shoes are gone. (00:04:30)
Character mistake: At Houdini's performance for the Kaiser, a German officer with the rank of Lieutenant Colonel (Oberstleutnant) is asked to assist. Houdini at first correctly addresses him as Lieutenant Colonel, but then incorrectly refers to him as Lieutenant several times after that.
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."
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.
Plot hole: After Jack's wife disappears for a couple of days, he receives a call from her cell phone from the cab driver who found it. Jack arranges to pick it up from a hotel. After he picks up the phone, its battery dies as he checks it, at 12:13pm. In the next scene with Jack, he's in a bar with the phone plugged into a charger; when it comes on, he checks it - the battery shows 3%, but the time is 9:13pm. He apparently wasted 9 hours when he's in pursuit of his wife's mysterious disappearance before plugging in the phone. A scene later, the time is now just a minute later at 9:14pm but the battery is now charged to 79%. (00:37:25 - 00:40:45)
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.
Things Were Different Then - S4-E16
Factual error: The car is referred to as a '73 Cadillac Eldorado. It has square headlights, and therefore is a '75 or '76.