Deliberate mistake: The Seal takes a shot with his suppressed pistol through a circular window in the hull of the ship at a hostage taker holding a hostage. When he fires through the glass it never breaks or shatters. Makes no sense how the bullet even passed through. In addition, windows in ships are really thick; it would've taken a few shots to get through and to neutralize the hostage taker. (00:33:30 - 00:34:30)
Thank You and Good Night - S1-E8
Deliberate mistake: In the Maisels' 1954 wedding reception flashback, Midge hired professional dancers who perform the "Bottle Dance" (where they slide on their knees). This famous dance, often performed at Jewish weddings and social events, was choreographed by Jerome Robbins for "Fiddler on the Roof," which debuted on Broadway in 1964. It did not exist in 1954 but, as an inside joke, while Midge watches, she says, "That's really good. They should do something with that."
Deliberate mistake: The police force in the town is the Gendarmerie, the standard issued firearm is the Sig Sauer P2022 in 9mm. The police officers on this show carry a Beretta and not the 9x19mm one which is the model 92fs, they carry a never issued Beretta 84 chambered in .32 acp or 9mm short. Plus they use some weird holster where the gun arches out and hangs low like a cowboy holster and dangles around. Easy for a suspect to gain control of the officers gun and this happened in this episode.