How do you recognize, and how do you deal with, a very drunk person?

Long story short, today while at my typical Monday night meetings at a Mexican fast food place, we came in contact with a very drunk man.
Two of my friends recognized it very early on, and mimed to the rest of us that he was drunk. But it took me 2 hours to recognize—the point at which he came over to us and started saying that we were “flapping our mouths” about Mexicans and how he was gonna have a fight with us if we kept it up.

From my point of view, up until that confrontation, he seemed like he was just a normal guy minding his own business, eating his meal, texting someone.

When the guy came up to us quite angry, the only thing that calmed him down was one of my friends threatening to call the cops on him.

When you’re in a public place, a restaurant, wherever, what are some signs you look for to see if a person nearby is drunk (or otherwise, far gone)?
If that person starts to confront you for whatever imaginary reasons, how do you react?