Plot hole: Apparently there is some confusion over the distance between Earth, Starbase 11, and Talos IV. When Spock first meets Pike on Starbase 11 he tells Pike Talos IV is only six days away. Yet when Pike (in the recording) speaks to the Talosians for the first time, he says he is from a star system on the other side of the galaxy. If Talos IV was on one side of the galaxy and Earth was on the other side, it would take hundreds of years at maximum warp to travel from one planet to the other.
Continuity mistake: As Veena (as the Orion Slave Girl) dances, the water in the pool is still, then in the Observation room, as Kirk and party watch, the water is disturbed. A moment later, it's flat calm.
Other mistake: When the transporter comes on to beam up Pike, the blonde ensign goes to face the transporter. As she does, she glances down at the floor to find her mark, and stands on it, looking into the chamber.
Revealing mistake: The shot of the castle on Rigel VII seems to be what Pike sees through his eyes, but in the next shot he himself is in the shot.
Deliberate mistake: At the very end, the Talosians send a final visual transmission of Vina and Christopher Pike, now whole and happy and reunited after 13 years, holding hands as they enter the Talosian elevator in the hillside. However, in this last shot, the elevator is still half-disintegrated, exactly as it was 13 years earlier when the Enterprise crew destroyed the hillside with a laser cannon. Within the context of "The Menagerie" storyline, this suggests that the Talosians never attempted to repair the elevator for 13 years (even though they continued using it). This incongruity is due to Gene Roddenberry cannibalizing his Star Trek pilot "The Cage," which contained zero footage of Jeffrey Hunter and Susan Oliver entering the intact elevator together (only the destroyed elevator). So, Roddenberry deliberately tried to "slip one by" the audience in this brief shot.
Suggested correction: There are reasons why the elevator would appear damaged. As the Talosians were in control of everything shown on the ship's viewer, the entire scene could be an illusion, or at least the elevator's condition may have been, with the Talosians choosing to allow the viewers to see the elevator in the same condition they last saw it. Just as likely, however, is that the Talosians truly never did reconstruct the elevator, as the whole point of their having a menagerie of other beings was an attempt to breed a race that could physically serve them, for their concentration on their mental powers had led to a complete inability and unwillingness to perform physical tasks (like repairing an elevator).
Still, as long as the Talosians are creating the illusion of Christopher Pike and Vina in their "restored" bodies, why not create an illusion of the elevator and hillside restored, as well? One big illusion of restoration, rather than a composite of dismal reality and happy-ending illusion? Again, to the point of my original post, the obvious incongruity is due to Roddenberry using the only happy-ending footage he possessed, that of Pike and Vina entering the half-obliterated elevator as they did at the end of "The Cage." Certainly, if Roddenberry only had the foresight to shoot Jeffrey Hunter and Susan Oliver entering the intact elevator, he would have used that footage instead. Any attempt to explain away the 13-year incongruity is mere wishful thinking.
This would qualify as a question, not a mistake. It is entirely plausible that the Talosians wouldn't bother to repair the elevator. It's also possible, as the previous correction points out, that the entire scene is an illusion. Remember, Captain Kirk sees Vina and Pike together on the planet literally moments after Spock wheels Pike out of the room. It's unlikely Pike had already been beamed down.
Revealing mistake: When the Talosians place Christopher Pike and Vina into the "picnic" illusion (in the countryside on Earth), Pike wanders around marveling at how real it all seems. Well, "real" except for the fact that Pike's body is casting 4 distinct shadows in 4 different directions on the ground, the result of studio set lighting.
