In Part I: The American Dream - Chapter Three: Playing It Bogart, if the player goes past Rico Muerte's room and goes down the hall where the boarded up doorway is, destroy it and follow where the blood trail leads. There's a dead body with a stake in his back, and a word on the floorboard that said "BUFF" written by him with his own blood. This is a reference to the TV series Buffy the Vampire Slayer.
In Part I: The American Dream - Chapter Two: Live From The Crime Scene, if the player throws a grenade into the big gap on the wall at the beginning of the level, the objectives will then say "I had declared a war against rats". The rats ahead will use their deagles to kill the player.
In the tutorial level, there's a 'Tar Cafe sign' that has a quote below it's name says "All your base are...". This is likely a reference to Zero Wing's English translation meme "All your base are belong to us".
Due to lacking the sufficient budget needed to hire actors, the staff, interns and associates of Remedy Entertainment ended up lending themselves to the likenesses of many of the game's characters. Most notably creative director Sam Lake provided the face model for Max Payne, and many of his relatives ended up being part of the game's cast, including his parents who posed in multiple shots as Nicole Horne and Alfred Woden.
In Part II: A Cold Day in Hell - Chapter Five: Angel of Death, Max can interact with a piano to play part of his theme, but shooting the lid prop renders the piano unplayable.