Drink plays an integral part in the story. For one thing, it gives these characters something to do. A great deal of the book is concerned with drinking in bars and restaurants and the kind of social performances that go with meeting people and flirting in bars. Drinking, and being drunk, but not disgustingly so, is a kind of unwritten code in the book. A great example of this is in chapter 3, where Jake, Cohn, and Bret all meet at a club, and Jake is introduced to Robert Prentiss. Jake's comment at the start of their brief conversation, that he "was drunk, not in any positive way, but enough to be careless," sums up one of the book's essential attitudes towards alcohol. It is an excuse for bad behavior.
There are many theses you could develop around these issues that could explore the role of drink in the story—drinking as a social ritual, or drinking as a plot device that propels the story, or drinking as a way of circumventing social constraints. One way into this would be to consider what Jake might mean by being drunk in a "positive" way.