The only episode I can recall Scotty drinking was "By Any Other Name" where he gets utterly toasted with the Kelvin, in order to "Overstimulate" the "Human-Like" responses.
He spoke about drinking on duty, though - even during working hours and crises. See "Tholian Web" where he thinks the cure for the week's space-sickness would go down better with Scotch. Although the cure itself was supposed to be an inebriant of sorts, so...
... a potential alcoholism problem brewing.
I guess this is the right forum for the question. After all, in TNG, "alcoholism" would probably not have existed: being addicted to ethanol would carry no bigger consequences than being addicted to oxygen, thanks to the wonders of 24th century medicine. Some TOS novels suggest there were 23rd century cures for both the associated problems and the addiction itself, too, and you'd have to be quite a pervert not to take those cures - more akin to a cancer victim deliberately skipping his miracle medicine than to a schitz skipping his happy pills.
The JJ take on the Trek universe is less likely to eliminate the dramatic potential of conventional alcohol addiction that way, though. And it's canonically free to choose that path, since aired TOS never said alcoholism wouldn't be a problem.