I really, really liked this. The backstory you give Filch here lends such depth and sympathy to his character, and works excellently within the context of what we know about wizard/muggle/squib relations. To that end, Albus' cheerful cluelessness about muggle matters rang very true - as did his slight bumptousness but fundamental kindness and courtesy; an excellent portrait of young Dumbledore.
I loved the way that these two very different men bonded over having done regrettable things in their past, and the progression of their relationship over time was delightful. You interwove this tale so very cleverly with other canon details, too - both the Knight Bus and the link with Tom Riddle via the orphanage was inspired.
Finally, there were quite a few lines that made me smile at the splendid language and choice of words. Here are a few of my favourites:
A fine network of lines around his eyes and the blank hostility in them whisper a mystery.
Magic literally saturates his being. He can tickle it with his fingertips and taste it in the air when he closes his eyes. He always thought that proximity to a squib would evince some kind of dismal sensory vacancy, but Argus Filtch doesn’t have that effect on him at all.
Argus blinks and then dissolves into wheezy giggles. ‘Christ, man! You’re a tactless bugger sometimes.’
He straightens Albus’ turquoise tie, smoothes the lapels of his new purple suit and brushes his fringe out of his eyes. ‘Go and see the boy. Give him the good news.’ <-Ouch.
Aaand, I'd better stop there, or I'll be quoting the whole fic back to you ;-) Suffice to say, I thought it was really excellent. :-)