The City on the Edge of Forever - S1-E29
Other mistake: When talking to Edith Keeler one evening, Kirk refers to a star in Orion's belt, pointing it out. The shot then cuts to a scene of the horizon. The sky is quite cloudy and the light from the sun is still lighting the horizon. The stars would not be visible.
Answer: After causing Norman to overload, all of the other androids shut down. The same could be said for the androids on the Enterprise.