The biggest plot hole in this episode wasn't Mendez, it was how everyone forgot about Morse code and didn't think of getting Pike to communicate that way.
MCCOY: We've learned to tie into every human organ in the body except one. The brain.
Except that McCoy's able to quickly rig a remote control for Spock just 2 years later in Spock's Brain.
Morse Code. Or the computer system Hawking uses. Granted, Hawking's tech wasn't available in the 60s, but Morse Code was. Johnny Got His Gun,
Yeah, that gets my vote for biggest plot hole or oversight.
My wife is a nurse and works with the disabled. She uses a cardboard chart with the letters of the alphabet arranged in a grid to communicate with her patients that can't speak or move. It is as low tech as it gets, but it works, and would have allowed Pike to communicate to Kirk, McCoy and anyone else much more than just the "yes or no" that his beeping chair light allowed in the episode.
Of course, Pike's inability to communicate was essential to the plot, so his being able to warn someone about Spock's plan would have ended the story pretty quickly.