Well, it if was to be in line with the mirror universe as pictured in DS9, it would have to be in some slave mine. The Terran Empire was long since defeated, after all. But ignoring that ....
A mirror episode wouldn't have been interesting, as the mirror Ent-D would still have been a dull ship, stuffed with all luxuries, with people committed to the high arts, and giving and listening to classical concerts, and so on. Only would they have been evil bureaucrats.
Mirror Picard: And yet you still refuse to give us your dilithium crystals? Very well. I have no choice but to sent a report in triplicate to our Emperor, who is not as forgiving as I am. And he will certainly put you under a trade embargo that will cover, but is not necessarily limited to, some of our cultural exports such as Mozart recitals, Shakespearean plays...
Mirror Data: Captain, they are beaming their entire planetary stockpile over into our cargo hold.
<Mirror Picard allows himself a tiny evil giggle before they warp away>