In the two-parter The Menagerie the Commodore Mendez on board the Enterprise is revealed to be an illusion.
There is, however, also a real Commodore Mendez on Starbase 6.
So when Kirk leaves with Mendez to go after the rogue Enterprise, we have to conclude we're already seeing the mirage. But this would imply that the Talosian's powers reach to Starbase 6 itself.
Is that meant to be implied?