When you come across Jack Lupino, in the graphic novel cut scene, he is holding an Uzi, however when you fight him, he is holding a double barreled shotgun shotgun.
The entire game takes place in the US, yet at least twice in the game we can see safety signs that say "no unauthorised persons beyond this point" (the common UK spelling of "unauthorized").
A .50 AE caliber Desert Eagle holds 8 rounds (7 in the magazine 1 in the chamber), not 12. A semi-automatic pistol is capable of holding magazines of potentially any size, and it is not impossible that an extended magazine was not being used.
The news anchor states that Max Payne is a "repeated felon" wanted for murder. A convicted felon cannot work as a DEA agent, but only Payne's fellow agents know he is DEA, and not a felon. He is undercover within the Mafia as a criminal.
The maximum number of sniper rifle rounds that can be carried is 19. Considering that each magazine holds 5 rounds, the maximum number of rounds should be a multiple of 5.