An functional alcoholic ( functional being the key word here) doesn't behave like your classic drunk.
As the following site says:
"They rarely miss work and other obligations because of their drinking, although it does happen occasionally, and they usually excel at their jobs and careers. Typically, they are clever and witty individuals who are successful in many areas of their lives. To all but those who are closest to them, they give the outward appearance of being perfectly normal."(
http://alcoholism.about.com/od/problem/a/functional.htm)
In DMC1 novel ( dubious canon?) he has a lot of problems: he has recurring nightmares related to his mom, he always seems in need to be thought as tought guy by the other mercenaries, dealing with killings and persecutions, lives in a seedy part of the city,etc....It was not an easy life!
It doesn't help either he drinks a vodka cog all alone in a contest, passes out in the street and awakes in a local woman's bed, where she is trying to have sex with him and he spurns her.
If he doesn't have a problem with alcohol, I don't know what problem he has.
Yes, Dante lives like a pig: only eats plastic food, sleeps all day and his place is a dusty mess.Yeah, we can excuse that with the idea he is a bachelor or whatever.(But apparently Trish lives with him in this dirty mess, she eats pizza in his disgusting desk and licks her fingers instead of washing her hands.Why she lives there? That's another story)
But as Sunny said before, Patty cleaned his mess over and over, and MAYBE she still does, so there is no excuse for so much empty bottles.
But Capcom only danced around taboo subjects without go further on there. And sure DMC is rich on taboos and unexplained matters.That's why DmC was seen as brutal to usual fans.