Continuity mistake: In 1912, Ray writes his letter in pencil. When it's delivered to Melissa in 1986, it's written in black ink. (00:20:15)
Continuity mistake: The water level in the dispenser rises and falls by itself several times throughout the episode. (00:08:05)
Time and Teresa Golowitz - S2-E18
Continuity mistake: As they talk, Prince and the pianist stand beside the apartment wall that's covered with Broadway show posters. There's no break in their conversation, but when the shot cuts, they're across the room in front of the window. (00:03:15)
Answer: They live in a totalitarian state where people who are deemed too smart (and therefore a threat to the authorities) are done away with. That's the point of the test, to eliminate potential troublemakers.
Brian Katcher