Plot hole: In Episode 1-7: The Serene Squall, the Enterprise is at the edge of Federation space, and it is stated that it would take two days for a message to be received by Starfleet. Later in the episode, they have no problem establishing a real-time connection to Vulcan, which, according to canon, is only 16.5 light years away from Earth.
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.
