When Max is about to leave his apartment in the morning, he shuts off the stove after a kettle starts whistling. The steaming item on the stove is an espresso pot, which does not whistle. A kettle is on the back burner, but it's not being used.
When Mona Sax arrives at Aesir Pharmaceuticals, she shoots through a door, near the lock handle, to open it. When she kicks the door open, the door handle, lock, and deadbolt are undamaged, and the deadbolt is not locked.
One of my favorite things to catch...When Natasha is being chased down the alley, she is no longer wearing high heeled, thigh high boots. If you take a look, you'll notice that the heels are gone and the boots are flat soled. Obviously, to make it easier for the actress to safely run.
In the end scene where Max stands in front of the two lamps on top of the Aesir building, he drops his pistol and kneels down; the gun falls in the yellow area with the grip towards the viewer. In the next scene you see the pistol laying more behind him in the black area and with the grip towards the building.
The film is set in New York. Yet when Max asks Alex "where are we going?" in Alex's car, a circular blue, white, and red sign is visible on a building in the background. It's a sign for the CAA (Canadian Automobile Association). A Canada Post delivery truck is parked in front of it. Alex's car also passes a TTC (Toronto Transit Commission) bus for the disabled.
(at around 46 mins) Max is driving through the city (supposedly New York City) when behind him through the windows of the car, you can see a "Tim Horton's" neon sign. There are no Tim Horton's in NYC (the nearest is in Syracuse, according to the company website), but they're all over the place in Toronto (where the film was shot.)
In the Roscoe Street Station bathroom, Max fires a revolver 6 or 7 times (you hear an echoing boom when the scene cuts to the mugger running on the tracks). Max is using a Taurus Judge revolver, which holds 5 bullets.
When Gunnery Sergeant. Jack Lupino is shown on video during his interview, his Gunnery Sergeant lapel pins are pointing in the wrong direction. The top should be placed vertically, with the single point up and the center of the insignia on a line bisecting the angle of the collar's point. Also, he is referred to as "Sergeant", as a Marine he would be addressed as "Gunnery Sergeant".
Jim Bravura has a detective's badge, and is frequently called a detective. Yet the door to his office and the name plate on his desk identify him as a lieutenant. In the NYPD, he would be called a lieutenant, even if he was assigned to a detective squad.
When the Marine is being interviewed about the the drug's effects, the rank on his collar is upside down, and he seems to have been promoted. The rank insignia are not USMC insignia. USMC insignia would have crossed rifles between the chevrons (pointed end at the top) and the rockers (the curved end at the bottom). The rank shown is the army Sergeant First Class (E7), and in the army he might be called a sergeant. In the Marine Corps the rank of E7 is a Gunnery Sergeant, and would be called Gunnery Sergeant or more informally Gunny.
Just before the fight with Lupino there's a guy coming behind and above Max and there's a slow-motion shoot out. The first shot comes almost in front of Max but the rest of them seem to hit the drugs on a table that's at least 2-3m on Max's right side.
At the shipyard, when BB is about to execute Max Payne, Max jumps into the water. BB and his partner shoot at him, hitting Max in the left leg. Max surfaces, takes the drug, stands up in a fit of rage, then limps away on the wrong leg. The bullet hole is now in his right leg.