^Except there's another continuity issue in Dark Mirror -- its assumption that if a significant amount of matter from one alternate timeline stays permanently in another, it would cause a catastrophic imbalance that would destroy much of the galaxy. This is contradicted by "In a Mirror, Darkly," where the Defiant from the Prime timeline stays permanently in the Mirror Universe.
Also, Dark Mirror treats the events of "Mirror, Mirror" as a classified incident that the Enterprise crew needs special clearance to find out about, while in DS9: "Crossover," Bashir says he "read about it at the Academy" (and he graduated only a year after Dark Mirror occurred, so it's unlikely there could've been a radical policy change in the interim).
I forgot about all that. Especially the matter transfer imbalance thing. Oh well.