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.
When Max crashes through the door of BB's office, the door is wide open, but almost closed in the following shot.
When Natasha Sax (Olga Kurylenko) is in Max's bed she has a sheet covering all the way down to her undergarments. On the next shot the sheet is lifted revealing her abdomen.
When Natasha is being chased down the alley, she is no longer wearing high heeled, thigh high boots. The heels are gone and the boots are flat soled. The alley way floor is seen to be clear but when she falls she lands on a sheet of cardboard.
When 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. Then the pistol is laying more behind him in the black area and with the grip towards the building.
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 Max Payne shoots out a couple of fire sprinklers, all the sprinklers in the floor go off. Each sprinkler is designed to be activated only if the temperature under that sprinkler melts its fusible link or if the sprinkler head is physically damaged. All the other sprinklers would not be activated unless a very large fire set them off by melting their fusible links.
In the Roscoe Street Station bathroom, Max fires a revolver 6 or 7 times (an echoing boom is heard when the mugger is running on the tracks). Max is using a Taurus Judge revolver, which holds 5 bullets.
When the Marine is being interviewed about 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.
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".
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.
The snowstorm is clearly staged, based on a shot of moths buzzing around a street light, which of course wouldn't be happening in the middle of winter.
In post credits scene with Mona she shows Max newspaper article about Aesir's IPO. It reports that it opened at $29, in the middle of its targeted range, and closed at $129. It reports this as an "unprecedented" 156% rise on its first day. This is actually an absurd 445% rise.
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.
As Max walks towards Alex's car, streetcar tracks appear in the road. New York City has no streetcar tracks, but Toronto, where the the film was shot, does.
In the first shots of the AESIR building, a Toronto Transit Commission (TTC) streetcar appears in the background.
The film is set in New York and to create the illusion NY taxis, police cars and a US post box are seen but 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, there is 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.)