I'm assuming the 'past-Quirrell' that Quirrell tells Hermoine about in Chapter 84 is the 'young man' that Amelia Bones believes is now Quirrell. (Is this reasonable?)

If that's the case, then one way of understanding the situation is this: Riddle assumed two personas---Voldemort and Light Riddle---in order to experiment with different ways of acquiring power. He found that the Voldemort-path was much more preferable on account of the loyalty he could obtain via the Dark Mark. The Dark Mark was so effective that the loyalty he earned as Light Riddle seemed negligible by comparison; thus he complains that he got no help from his 'allies'.

So Riddle retired his Light persona by faking his own death and continued only as Voldemort. Now that he sees Harry as a potential puppet, he wants to ensure that he/Harry have loyalty comparable to that secured with a Dark Mark. He therefore calls for a 'Light Mark' in his speech before Christmas.

EDIT: Of course 'Light Riddle' (if he existed) and Voldemort would have looked different; Minerva remembers Voldemort as snake-like. If the above is right, then Voldemort's disfiguration would have to be a disguise rather than real damage from Dark Rituals.