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.
Other mistake: William H Macy is holding his iPhone upside down during a conversation. (00:49:18)
Other mistake: When Hannah turns on the magnet, it's so powerful that it pulls the sword out of Donovan's hand from across the room, but no other metal object is affected.
Other mistake: Officer Marvin Sandeford has 25 years plus on the job as an NYPD Officer. He was on the job during 9/11, but he doesn't wear the WTC (World Trade Center) commemorative WTC bar above his badge on his uniform, which is a mark of honor for the NYPD. (00:39:27)
One Ocean Closer to Destiny - S1-E6
Other mistake: Near the end, Spencer and Alex make love and there is a brief shot of her feet lying on top of his. The scene then cuts to them lying near each other. The problem is, the way Alex is lying would mean her feet would be pointed sideways and unable to appear like they do in that brief shot. She would have to be lying on her back in order for her feet to appear the way they did.