Umm, doesn't the cap linked above expressly show
the actors of Lindstom, Krasnovsky and Chandra? Just before Kirk enters the bar for the first time? They are all wearing their Captain-style dress jackets, too, suggesting the characters are part of the board already (as Captain Kirk never felt an obligation to dress up until he got involved in the trial - nor did Commodore Stone). And the court clerk or bailiff or whomever in the special red jacket is also seen on the foreground.
The way it's edited, there might not be a continuity error - but there definitely is an error in Kirk's assessment of the situation. He believes the members of his court martial board are "proceeding to SB 11" when they are in fact aboard the station already, and have been since before the first stages of the inquest! Somebody appears to be misleading him on this issue...
...Which isn't all that unexpected when everybody quite consistently appears to be opposing him and rigging the game against him.