Corrected entry: After Kirk and Spock's identities are revealed, they are taken to a prison cell. However, the Organians are a race of pacifists who abhor any act of violence - this should presumably include the act of incarceration. As such, there should be no prisons on Organia. Moreover, the Klingons are not stone masons; the prison cell shown in the episode is architecturally consistent with the other buildings on the planet so it was not constructed by Klingons (especially so quickly).
Corrected entry: Kirk and Spock are thrown into a prison on planet Organia by the Klingons. The Organians, however, are a peaceful community where prisons make no sense.
Correction: The Organians faked their entire civilization, including both their own appearance, culture and buildings. As it is all placed there to fool visitors, a jail is not out of place at all, but helps maintain the masquerade.
Correction: This is purely speculation. Being pacifists doesn't preclude them from having a jail cell, especially since the entire town was created for the benefit of outsiders.