This is one of my favorite Next Gen books, My favorite Duane book after Spock's World, and My favorite Mirror Universe story. And best of all it's not the least bit incompatible with tv show continuity since there's no reason why there can't be two different mirror universes.
But there are contradictions on the Prime-Universe side too. There's the difference in secrecy that rfmcdpei mentioned, and there's the problematical claim about a galactic-scale cataclysm resulting if matter from another timeline is permanently transferred across -- which has been definitively contradicted by "In a Mirror, Darkly" if nothing else. (And by Forgotten History, on a planetary scale.)
That second could be fudgeable. A method of interuniversal travel that depends on hacking about the strings that bind the universe together in space and time could be plausibly expected to have consequences more traumatic than mishaps with transporters or godling-populated wormholes.
But what does it matter? Continuity is nice when you can get it, but it's all just a bunch of made-up stuff anyway. All that matters is if the story is enjoyable.
The character of Security Officer Deanna Troi alone was worth it. I wonder if Duane did write the character after seeing "Face of the Enemy". Duane certainly managed to make Troi's duplicate rather unexpectedly terrifying, and with style--the paraphrase of an Einstein quote--"Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. THAT'S relativity."--delivered to LaForge in the agony chamber was noteworthy.