If a Shochet under the influence of alcohol slaughtered meat is the meat kosher for consumption or does the fact that he is drunk make him equivalent to a Shoteh (a mentally incompetent person) thereby disqualifying his Shechita?
A drunk person should not slaughter, but if he did anyhow, as long as the technique was proper, the slaughter would still be good. In fact, even if he was so completely drunk as to be not cognizant of his actions ("as drunk as Lot") and he'd have the same halachic status as someone insane; the halacha is if someone insane did slaughter, and used the proper technique, it would still be kosher. (Rambam laws of slaughter 2:12).
The Shulchan Aruch (Yoreh De'ah 1:8) states that one who becomes as drunk as Lot (see Genesis, ch. 19) may not slaughter. One who has not reached this stage of inebriation may slaughter at the outset. The Rama rules more stringently, stating that a person should never slaughter when drunk, for it is likely that he will disqualify the slaughter.
Simlah Chadashah says that someone who is as drunk as Lot is the same as the שוטה.
He also adds that someone who is not quite that drunk yet may not slaughter ab initio, but if he did and it is certain (if he says he is certain or someone was observing him) that there was no דרסה (undue pressure in שחיטה) then it is allowed.
A city שוחט should not be drunk ever (1:36, 1:7) because he needs to be ready to kill at all times; if he is not, then he may slaughter drunk. מטה אשר on the spot, based on שמלה חדשה later (18:7) that the habitual drunkard's limbs are perpetually heavy, and there is a חשש דרסה always [שמלה חדשה was discussing how to check the knife, and the drunkard will not be able to do that so efficiently]. Additionally, מטה אשר writes that since many times a בדיקת הריאה will require some sort of פסק -- someone who drank a רביעית may not decide הלכה.