When Charlie first flashes her badge, she's holding it upside down just as Castiel did in his first attempt at being an FBI agent, in Free to Be You and Me (2009).
Charlie refers to her djinn-induced video game dream as "an infinite loop. Like, Pac-Man without level 256." It is an allusion (as is the episode title) to the iconic arcade game and its final, unbeatable level.
Dean introduces himself and Charlie as FBI Special Agents Hicks and Ripley, a reference to Dwayne Hicks and Ellen Ripley in the film Aliens (1986).
When Charlie is in the elevator she tells Dean "come with me if you want to live". This line is said in every film in the Terminator series and Charlie is carrying the same gun favored by Sarah Connor.
When Charlie asks, "are you going to invite me into your dungeon, or do I have to answer your questions three, first?" It is a Monty Python and the Holy Grail (1975) reference. The Bridgekeeper asks three questions before allowing anyone to cross. It is also a Dungeons and Dragons reference. Charlie is a geek, so she would know both.