Number One's briefing room comment "So we just THOUGHT we saw survivors there" should not have been in the first person plural (we), since Number One herself was on the Enterprise during the referenced incident.
When Number One is in the transporter room, she is wearing a bright shade of red lipstick. Seconds later, when she materializes in Captain Pike's cell on Talos IV, her overall makeup is lighter, with a much lighter lipstick, matching Yeoman Colt's shade.
When fighting the Kaylar in the illusion of Rigel 7, Pike holds the Kaylar off with a staff as he backs up the stairs. The staff appears to have a metal blade. When the blade is pushed against the Kaylar's body, the blade flexes like rubber.
At the end, Kirk asks Pike if he wants to go down and live on Talos IV and Pike signals "yes." Pike, due to severe injuries, can only signal "yes" or "no" using a light on his wheelchair. Everyone just finished watching transmitted video documenting Pike's encounter with an alien species (years before) which is able to create illusions, even at a distance of miles. When Pike signals "yes," no one questions if this itself is an illusion.