The title "The Bottle Job" is a reference to the industry term "bottle episode", which refers to an episode that is shot on a limited budget, using preexisting sets. In this case, most of the episode is set in the bar where the Leverage team meets their clients, and Nate's apartment upstairs (which the team uses as their office).
The crew refer to the first con they pull on Mark Doyle as "The Wire," which is a real confidence game. As Nate says, they only do part of The Wire (he refers to it as "The Wire in a bottle"); usually, the set up with a delayed feed is used to hook the mark into giving the con artist money to lay a bet for them. This con was also famously used in the film The Sting (1973), where it was played on a mark named Doyle Lonnegan. This episode's mark, "Mark Doyle," is likely named after him.
The song playing during the card game, "Can't Go Home Again," was originally written for and used in the season one episode The 12-Step Job (2009).
The announcer of the basketball game refers to one of the basketball players as Arnie Risen. There is a real Arnie Risen, who played for the Celtics in the 1950s. He was a center, and is a member of the Naismith Basketball Hall of Fame.