So, after a dutiful look at some literary theory about vampires and mirrors (I mean, it was Lacan, right? I did my duty!), here are some more rambling thoughts about mirrors and folklore that in my mind are interesting intersections with Stoker's Dracula.
Let's start with the Greeks. Two thoughts come to mind:
Medusa. Remember Medusa? (Theoi.com is a good source to refresh your knowledge.) She was the monster with the snakes for hair whose gaze was deadly (and who surely is part of the inspiration for the super-fabulous weeping angels of Doctor Who). So, how can a hero ever hope to defeat Medusa if merely looking at her will get you killed? You use the power of a mirror to defeat her! Perseus was able to slay Medusa because he guided his deadly sword by looking at Medusa as reflected in his shield (a gift from Athena); he beheaded Medusa and then used her head as a weapon in turn; the deadly power of her gaze persisted even after death. Poor Perseus: imagine if he had to battle Dracula - he could not use the power of the mirror to avoid Dracula's gaze, ha ha. And we know there is something funky going on with the power of Dracula's gaze - he has those WEIRD RED EYES. There are also numerous references to the power of the evil eye in Stoker's novel (cue eerie music…).
Basilisk. Medusa was not the only one with a deadly gaze in Greek mythology; the basilisk was also able to kill with a look and had to be defeated with a mirror, because you could cast the basilisk's own gaze against itself. Thanks to Hermione Granger and Harry Potter, this is an old myth that has taken on new life! Here is a wonderful illustration from a 1501 edition of Aesop's fables which also contains all kinds of animal legends from the bestiary tradition, beyond just the canon of fables - and you can see here a knight with his shield mirror, turning the gaze of the basilisk back upon itself! (The weasel is also making a frontal attack, biting the basilisk on the foot; the accompanying poem is about a weasel, reflecting the basilisk-and-weasel legend from the bestiary tradition; full page here). Now, I have always personally suspected a cross-influence in Greek between the scientific etymology of basilisk meaning "royal, kingly" (from basileus, king; hence the regulus snake in Latin) and the word for the evil eye in Greek, baskanon (compare Latin fascinum, English fascinate, etc.), which is a sound-alike word. We'll never know, of course... but I imagine if I had been an ancient Greek person obsessing about the evil eye (as they did), then I would definitely have felt a connection. :-)