When in Rome - S1-E3
Character mistake: Nobody in this scene knows how to dance the tango that is playing. (00:16:35)
In the Waiting Room of Estranged Spouses - S2-E6
Character mistake: The former Marine, Spenser, refers to himself as a soldier. A Marine would never do that.
Character mistake: The Captain's medal ribbon bar is sewn onto his uniform back to front, with the 1939-45 Star on his left and the 1939-45 War Medal on his right.
Suggested correction: This is explained in the final episode, as he took somebody else's medal ribbon bar in order to get into an event only open to "decorated" officers and hurriedly put it on the wrong way round. However, this is also a mistake. Although the Captain never left Britain, he would still be entitled to the War Medal and Defence Medal, so would legitimately have two of the ribbons he wears. And having campaign medals does not make one "decorated" in any case.
Character mistake: In Season 5, Episode 4 ("The Heart Attack Boys"), Abishola twice gives Christina an injection without swabbing her skin with alcohol. Abishola is an RN and would never make that mistake.