Well, it's the Defiant from the "Tholian Web" and thus from the "normal" universe.
Having future technology in the past is indeed problematic but let's not forget that the story ended with a cliff-hanger and that a follow-up story to "In a Mirror, Darkly" was planned for the fifth season.
Nobody in the Terran Empire analyzes the Defiant, whoever possesses her uses her as a weapon. And a weapon can be destroyed in a battle. I am sure that in the follow-up story this would have happened. Unless the people in charge wouldn't have cared about timeline stuff because they enjoyed the old sets too much.
After all that was the true purpose of In a Mirror Darkly, it was simply the third TOS homage story.
About continuity, I liked that it achieved the impossible en passant, to portray TOS technology as being more advanced than ENT technology.