The picture in Hale's office shows B-52s that are or were located at the 309th Aerospace Maintenance and Regeneration Group at Davis Monthan Air Force Base in Tucson, AZ. Sometimes referred to as "The Boneyard," it is where many military aircraft are stored until reused or destroyed. There is no obvious reason why the picture is in his office (the picture is from Wikipedia's entry on the base).
Ashburn's yearbook is Sandra Bullock's actual 1982 yearbook from Washington-Lee High School in Arlington, Virginia. The art department digitally manipulated Bullock's picture to include glasses and braces, neither of which she had in her original high school senior portrait. They also took out all the signatures within the book.
Originally, Melissa McCarthy was unable to do the film due to overlapping commitments for Identity Thief (2013) and Mike & Molly (2010). However, the day after the former wrapped filming, McCarthy commuted to Los Angeles and Massachusetts, enabling her to do both.
Before The Heat (2013), the last comedy about female law enforcement partners was Miss Congeniality 2: Armed and Fabulous (2005), which also starred Sandra Bullock. The Heat (2013) marked Sandra Bullock's third role as an FBI Agent, with the previous ones being Miss Congeniality (2000) and Miss Congeniality 2: Armed and Fabulous (2005).
The first 20th Century Fox film since mid-2010 to have its 35mm release prints on Kodak film, following Kodak's June 2013 agreement with Fox to supply film to its motion picture and TV studios. The studio had previously switched to printing on Fuji.
In the scene where Mullins breaks into Ashburn's house and is looking at her yearbook, just after Mullins hugs Ashhburn and starts talking about her pajamas, you can see a tour bus drive by the window in the background.
The trivia items below may give away important plot points.
Craig (Dan Bakkedahl), whom other characters repeatedly assume is a villain because he is an albino, is a parody of the "villainous albino" trope that has become increasingly prevalent in movies since the 1980s. These movies include: Lethal Weapon (1987), Cold Mountain (2003), Hellboy II: The Golden Army (2008), The Da Vinci Code (2006), and End of Days (1999). Early in The Heat (2013), there are visible clips from two movies that have albino villains, The Matrix Reloaded (2003) and Foul Play (1978), as a foreshadowing of the Craig character and the criticism he represents of the idea that all movie albinos are evil.