When the character Frank Wheeler (Leonardo DiCaprio) is having lunch with Bart Pollack (Jay O. Sanders,) you'll notice around the 52:24 mark that Bart lifts his martini glass, downs it, and he places it back on the table (empty except for the olive.) On the next shot back to Bart, the glass is full. Then on the next shot (as Bart takes a bite of food,) the glass is empty again. All of this takes place within a few seconds, so there is no way that this is no way that this can be a newly brought martini.