Factual error: Bill wears four medal ribbons, in order: Diamond Jubilee Medal (awarded to all people with five years' service in a British uniformed service in 2012), Golden Jubilee Medal (the same in 2002), Queen's Police Medal (a very prestigious award, a handful of which are awarded every year to long-serving police officers for exceptional service) and Police Long Service and Good Conduct Medal (awarded for 20 years' unblemished service in the British police). Not only are these in the wrong order (it should be QPM, Golden Jubilee, Diamond Jubilee, LS&GCM), but he's not entitled to any of them! He's an American who hasn't previously served in the British police. A chief constable's uniform doesn't just come with medal ribbons for the look of it; only those that have been earned may be worn.
Factual error: Alice and Kate's little reunion underwater is disrupted by policemen that fire at them, and one of the shots reaches the transport truck, ignites it and makes it explode. The scene is baffling; forgetting the complete disregard for fellow policemen in the vehicle, how would bullets have enough strength to penetrate into an armored truck deep underwater, reach a critical weak point from that angle (the truck is upright, they should be barely get to shoot the roof of it) and still underwater cause inside the completely immersed vehicle a spark that would ignite fuel and make the whole truck explode? (00:31:45)
Factual error: After escaping from Danzig, Grzegorz and Konrad flee to Warsaw, then to the eastern, Soviet-occupied part of Poland. They then make their way on foot right across occupied Poland and Germany to join British forces at Dunkirk, a distance of over 1,000 miles. Not a likely journey on foot at any time, let alone across hostile territory in the middle of a war.
Other mistake: Crowley shows acute discomfort while inside the church with Aziraphale and the Nazi spies as he is on consecrated ground. However, (spoiler alert) once the bomb destroys the church he is perfectly comfortable. The key word here is "ground" - it is the land upon which the church stands that is consecrated, not the building itself. (This allows churches to be rebuilt if they are demolished or destroyed.) Crowley should still be in considerable discomfort after the church has been blown up.
Factual error: George Wigg MP wears an RAF tie. Wigg served in the Royal Tank Corps and the Army Educational Corps, but he was never in the RAF. Few men would wear a regimental tie to which they weren't entitled, least of all someone in the public eye, where it would be immediately picked up and ridiculed. Especially given this is set only 17 years after the war (and only just after compulsory National Service ended) at a time when most men were entitled to wear some sort of regimental tie and recognised fellow veterans by the design of their tie.
Factual error: When Bachu talks to Pavel during their lunch, two bottles of vodka are visible. Top of the bottle should read: RUSSKAYA, however, it's misspelled and reads "RUSSKAVA." Other issue with those bottles - in the center it should read in Russian "Русская Водка", however, although "Водка" spelled correctly, the "Русская" is misspelled and ends on "ерская", which is incorrect. (00:30:26)
Continuity mistake: As Ricky Gervais walks by the school where his nephew is, a "chubby little ginger" shouts "pedo" at him. He stops and holds one of the bars of the railing, third from the pillar. In the close-up, you can count more bars than that, showing he is in a different position altogether. (00:07:00)
Continuity mistake: Elisabeth Shue is talking to Homelander by her car. As she gets her baby out of the car, she says "can we please just talk later" and has a muslin hanging over her right shoulder, turns around, and from the reverse angle the muslin is bundled up in front of her, not over her shoulder at all. Then the angle changes again and it's back where it was before.
Continuity mistake: A group of people are standing before a door with full glass inserts. It has a thought processor for access. Once the group defeats the processor, they open the doors. But the doors are now solid wood, not with a glass insert. (00:29:20)