Collecting the letters found in certain levels as Biker will unlock additional dialogue when talking to the characters in the basement at the end of chapter 19. While normally they will refer to their scheme as just a game, when all of the letters have been collected, they will reveal a much deeper conspiracy present within the game.
Contributed by broenheim
The fish mask, Phil, which translates the game dialogue to French, is in reference to Phillipe Poisson, also known as Phil Fish, the French-Canadian game developer known for the creation of the indie game Fez.

While the translation is mostly aesthetic, the mask does add some unique dialogue for the ending of the Bonus Chapter Highball:
"Salut, je suis Wiley Wiggins! Bienvenue a fantastic arcade!"
which translates to "Hello, I am Wily Wiggins! Welcome to Fantastic Arcade!"
This is in reference to the festival "Fantastic Arcade", which named Hotline Miami as "Most Fantastic" in 2012.
Contributed by G-Haven
The protagonist was originally a fat man wearing a pig mask, as seen in the trailer. Unused sprites of this character are still in the files.
Contributed by DeerBoarDude
Hotline Miami was heavily influenced by the 2011 film "Drive" directed by Nicolas Winding Refn. Refn is also given a special thanks in the game's credits.
Contributed by KnowledgeBase