Writer Robert Hewitt Wolfe wrote the fall of the Terran Empire into the script as an analogy for the fall of the Roman Empire to barbarians and the Chinese Dynasty to the Mongols. He also wanted to illustrate that if an Empire is as brutal as the Terran Empire was in Star Trek: Mirror, Mirror (1967), there were probably reasons why it was so brutal and he wished to convey the message that, in such circumstances, one cannot change things overnight, and even the actions of Captain Kirk can have severe consequences.
Prior to the establishment of the history of the televised mirror universe, a mirror version of O'Brien appeared in the novel Dark Mirror, depicting a mirror universe in which the Terran Empire had survived well into the 24th century. That version of O'Brien served as a conn officer aboard the ISS Enterprise (ICC-1701-D) from 2364 until at least 2367.
After "Crossover" aired, there was a great deal of discussion about how sexy and alluring Nana Visitor was as the Intendant, with the costume she wore garnering a great deal of attention. According to costume designer Robert Blackman, the general consensus amongst fans was that it was the revealing nature of her costume which gave Visitor this new level of seductiveness.
The teaser scene in which the two Klingon soldiers board the runabout is intentionally shot from extreme angles, which director David Livingston compared to essentially shooting up the actors' noses. He did this to emphasise how different things were in the mirror universe.
The trivia items below may give away important plot points.
This is the only mirror universe episode in which the crossover is made via the Bajoran wormhole. All subsequent episodes show the crossover being made by way of a specially adapted transporter. The non-canon novel Fearful Symmetry claims this is because the crossover in this episode was a deliberate attempt by the Prophets to connect the two universes.