In general, it is a very good idea to be suspicious of first-person narrators. They usually tell a completely subjective story from their own point of view and have every incentive to mislead the reader and make themselves look good.

I would agree, however, with the other answer, which understands Jake as reliable. His dead-pan, journalistic reliance on facts as well as his relentless refusal to sugarcoat his situation or hide his own often negative emotions causes us to trust him as a narrative voice. He doesn't disguise his impotence (physical and emotional), his pain, his sense of alienation, his disgust with Cohn, or his deep admiration and envy of Romero. We know he longs for a lost world where everyone had a place, but he doesn't pretend that is going to return ever again in modern society.

Jake most often uses blunt, simple language which goes straight to the point. For instance, he tells the more romantic Cohn:

You can’t get away from yourself by moving from one place to another.

This statement is one example Jake's straightforward character. He is the quintessential Hemingway hero, bearing his pain stoically while never pretending it isn't there. Because we know he tries as hard as possible to be honest about his situation, we trust him as a narrator.

Jake can be considered to be a reliable narrator. He reminds readers of Nick in Gatsby-in the way he tends to withhold instant judgements. He is a keen observer and does not spare himself in his honest assessments of characters and their motivation.

He is meticulous in his accounting of money-he notes how money is spent, the value of what is bought, and the frequency with which it is spent. This honesty lends to his perception as a reliable narrator.

Jake does not sugarcoat his views for anyone, even Brett, whom he loves. Her flaws are given as well as her strengths. Jake's own flaws are readily available to the reader , as well. Jake inspires trust in readers , and therefore comes across as a reliable narrator.