As was common in early TNG episodes, Chief O'Brien is seen incorrectly wearing Lieutenant's pips.
The atmosphere on the planet seems to have a variety of temperature regions. They mention gaseous nitrogen and methane and liquid neon, which could not possibly be present together. Also, part of the surface is frozen methane, but there is a pocket of room temperature air just above it.
Geordi says the planet's surface is -291 degrees Celsius, but absolute zero, a state of zero thermal energy and the lowest possible temperature of anything, is -273 degrees Celsius.
If you look closely at the mission patch on the space suit, you will see that it is actually the Apollo 17 mission patch with the names Cernan, Evans, and Schmitt clearly visible.
Data: (rolling craps) Baby needs a new pair of shoes.
Texas: (playing craps) Ah! Snake eyes!
Data: (to Riker) Single digits on each cube are not at all desireable.
Riker: (to front desk assistant manager) This planet-–what do you call it?
Assistant Manager: (incredulously) Earth... what do you call it?
Worf: We call it Theta 8.
Assistant Manager: How charming.
Riker: Looks like the poor devil died in his sleep.
Worf: What a terrible way to die.
Mickey D: Should have listened to me... no woman is worth dying for...worth killing for, but not worth dying for.
Picard states that Fermat's Last Theorem had gone unsolved for 800 years. In reality, it was solved in the 1990s by Princeton University Professor Andrew Wiles just a few years after this episode aired.
When Picard reads the opening line of the novel The Hotel Royale he says, "'It was a dark and stormy night'...not a promising beginning..."
These words are the actual opening of the 1830 novel "Paul Clifford" by Edward George Bulwer-Lytton, which is considered by some to be the worst novel ever written. The line is a cliche as the opening for a bad story, a situation that has been parodied many times in the comic strip Peanuts. Each year, the English Department at San Jose State University has sponsored a Bulwer-Lytton Fiction Contest, in which contestants are asked to contribute the opening sentence to the worst of all possible novels.
Picard: Curiouser and curiouser...
Quoting from Lewis Carroll's Alice's Adventures in Wonderland. The complete line is, "Curiouser and curiouser!" Cried Alice (she was so much surprised, that for the moment she quite forgot how to speak good English). "Now I'm opening out like the largest telescope that ever was! Good-bye, feet!"
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