Under the Cloak of War - S2-E8
Other mistake: The Klingon ambassador burns his hand when grasping a goblet. It is the palm of this hand that is burnt. When he is treated in Sick Bay with a dermal regenerator, it is being used on top of his hand.
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.
