After Dr. Lester, in Kirk's body, first arrives on the bridge and starts issuing orders, a wide shot of the bridge and viewing screen clearly shows a blond crewman (stock footage featuring Bill Blackburn) other than Chekov at the navigator station. At the tail end of this shot, Lester/Kirk specifically addresses his order to Chekov. In the very next shot Chekov is suddenly at the navigator station to hear the rest of Lester/Kirk's order.
At the hearing, Spock states "You do not belong in charge of the Enterprise, and I shall do everything in my power against you." When Kirk orders those sentences replayed, the recording -- though it is Spock's voice -- is clearly not a recording of what he just said, but of Spock repeating those sentences, probably in post-production. The inflection is different, and the words come out more rapidly.