It seems to me many of the similarities between the Dark Mirror and your counterpart of choice have arisen largely from FSA's hectic storyline development. Judging from Aonuma quotes, early on the game was intended to be one of the first games in the timeline, presumably before Ganon had been added to the story. Considering the backstories of both FSA and TP's mirrors, perhaps they were originally meant to be one and the same? Of course, FSA is now much later in the timeline, coming after TP, and any connections between the mirrors was shattered to pieces by Midna.

What about the Magic Mirror, then? FSA was at one point going to tell the story of the Imprisoning War from LttP's backstory. There are a few similarities to these two mirrors also, as they both bring darkness to light (LttP moving something from the dark world to the light world, FSA literally creating dark clones of people), and it's just one more on the long list of connections between the two games. This one is also doubtful, however, as Miyamoto forced the development team to change the story, wanting the Imprisoning War to be a seprate event. This makes some of the connections between the two games less clear, and while important things like the trident are obviously still the same, the mirrors are less obvious.
Of course, there is one mirror that everyone has overlooked. And so, with great joy, I present my new mirror theory!
The Dark Mirror is...
(dah-dah-dah-DAHN!)
The mirror from The Adventure of Link!
You know... that one... the one under the table...
This theory offers some explanation to the mysteries in AoL. For example, where exactly did the last boss come from, anyway? The mirror under the table, of course! And it makes sense that the mirror would be in the possession of one of the town elders, who may be descended from the sages themselves! One problem with this theory is that the mirror never seems to cause any trouble while you have it, but come on! You pick up the mirror and hand it to the town elder! When did it have the time? Besides, that was probably when it brought the darkness in Link's soul to life. From there on it lay dormant in him, until the perfect moment to attack came!
The elder also teaches you the LIFE spell for recovering the mirror. He must have been concerned about your well-being after carrying such a dangerous object around!
Anyway, the mirror is obviously very powerful. Look...

It allows Link to speak! Clearly, this is not an ordinary mirror!
