In the opening scene at Wrigley Field, Jon Favreau makes a reference to going to "Wiener Circle" to have hot dogs after the game. Wiener Circle is a hot dog stand famous for the staff yelling and cursing at customers when they order. If the customer does not return the favor, they do not take your order. Generally, though, this only happens late at night on the weekends.
When Joey Lauren Adams is bathing the kids she pulls the soap out of one of their mouths and says, "We'll save that for when you're twelve." This is clearly a nod to A Christmas Story where Peter Billingsly, Joey's husband in The Break Up, plays Ralphie and gets a mouth full of soap at twelve.
Toward the end, Vince Vaughn uses his favorite line when he tells the passengers on his tour boat about getting hopped up and making some bad decisions. He uses the same line at the beginning of his role in The Wedding Crashers.
The French movie poster hanging above the TV in Jennifer Aniston and Vince Vaughn's condo, "Un Tueur dans la Foule" is for the 1976 movie, "Two Minute Warning, starring Charlton Heston which was also released by Universal Studios.
The Old 97's are performing their song 'Time Bomb' while Brooke is waiting for Gary at the concert. The Old 97's also played the same song during the opening credits of another Vince Vaughn movie, Clay Pigeons (1998).
John Michael Higgins plays a member of an acapella group called the Tone Rangers in this movie. Several years later, he goes on to play an acapella competition commentator in the movies Pitch Perfect and Pitch Perfect 2.
Jennifer Aniston walks naked at her home but her breasts were strategically hidden but not her bum. Karen Gillan did a nude scene in a similar manner in Not Another Happy Ending (2013). Karen referenced The Break-Up herself later on in Selfie: Perestroika where she played Eliza Dooley.
The trivia item below may give away important plot points.
The original ending featuring Gary and Brooke running into each other at an art fair each dating someone that looked identical to the other (Brooke's date looked like Gary, and Gary's like Brooke) was scrapped when it tested poorly. A new ending was filmed with the same result but featured Gary and Brooke running into each other on the street alone. In both versions the two remained broken up.