Episode #3.1 - S3-E1
Continuity mistake: At the wedding, Arthur leaves the table looking for Tommy and Grace, leaving his suit jacket. The next scene, he appears at Tommy's door wearing the jacket. (00:14:20 - 00:15:30)
Episode #3.2 - S3-E2
Continuity mistake: John and Polly are talking in his office. He is wearing a ring on his left hand, then a few seconds later he is not.
Episode #3.1 - S3-E1
Continuity mistake: When Michael and Charlotte are alone together, the size of the flame on the candle differs depending on who is in shot.
Other mistake: There are multiple spelling mistakes in the sub-titles: Saltley is spelled Saltely, Balsall Heath is spelled Basall Heath, and Changretta in Italian would be Ciangretta.
Factual error: Filter cigarettes didn't appear before 1935, but here everyone seems to be smoking them.
Factual error: Mosley is portrayed as forming the British Union of Fascists in 1929 or 1930. In fact, he formed the New Party in 1931. The party failed to win any seats in the 1931 general election (with Mosley himself losing his seat) and Mosley then formed the British Union of Fascists in 1932.
Episode #3.1 - S3-E1
Visible crew/equipment: While Tommy is making a toast at the dining table, a boom mic can be seen at the top of the frame for a brief second. (00:19:30)
Episode #1.1 - S1-E1
Factual error: Ada is watching a movie and when asked "tell me the man's name" says "Rudolph Valentino." Valentino was largely unknown in 1919, only appearing in bit parts. She is also eating popcorn. This was not done in movie theaters until the 1930, unless you brought your own. Only street vendors sold popcorn.
Suggested correction: This is from episodes #1.2 and two separate mistakes. But being "largely unknown" doesn't mean she couldn't know his name. And who's to say she didn't buy the popcorn from a street vendor? You don't see others eating popcorn, so there's no suggestion she bought it there.
He used the name Rudolph Valentino for the first time in 1921.
That's not true since he was credited as Rudolph as early as 1917.