Other mistake: The episode begins with the Enterprise unable to contact in timely fashion the Federation, because there are 2 days of delay in communications, which puts Pike in a bind since apparently he needs authorization to get in non-Federation space (which kinda undermines the premise of the show). However, later in the episode, the Enterprise contacts the Vulcan facility on Omicron Lyrae without the slightest difficulty or delay.
Other mistake: Throughout season 1: The emergency workers are sometimes seen wearing a black jacket with an English spelling mistake on it. It reads "FIRE EMS RESOUE." Obviously the last word should be "RESCUE."
Other mistake: The King's ship has no steering devices, steering wheel/pin, no steerman, and no crew. (00:26:00)
What Happens in Atlantic City - S2-E2
Other mistake: Early in the episode, the team is driving south from NYC to Atlantic City on what appears to be the Garden State Parkway when they pass mile marker 19.4, which is well south of the exit for Atlantic City (exit 38).
Other mistake: The police vehicles are marked with the fictional 'Greater London Police', but in speech the characters refer to the real Metropolitan Police.