The first time that Picard orders "Tea. Earl Grey. Hot." from the replicator. Due to ship-wide malfunctions, that order is unsuccessful.
This is the episode with Riker's iconic line: "Fate protects fools, little children, and ships named Enterprise." This is based on a statement by 19th-century German Prime Minister Otto von Bismarck: "God loves children, drunkards, and the United States of America."
This episode is the first in the series to mention Picard's interest in archaeology.
First appearance of the Iconian gateway. A second Iconian gateway would be discovered 8 years later in DS9 To the Death (1996).
When Picard, Data, and Worf are on Iconia, several scenes keep repeating in the Iconian transportation device. During the cycle, one scene that appears several times is a picture of a building with two rounded towers. This building is the City Hall in Toronto, Ontario, Canada.