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: 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.