At the end of the car chase, when the burgundy Cadillac's left front tire blows out, the hubcap can be seen flying off in a close-up. When the car flips over, the hubcap is back on.
During the opening scene with a shop bomb exploding, a man next to a red car is seen collapsing unconscious, but the next frame sees him crawling on all fours.
When Chow Yun-Fat's character is questioning the Chinese guy in jail his hand is holding the guys chin, then his throat, then his chin.
The NYPD's 13th Precinct does not cover Chinatown, the 5th Precinct does.
They worked out of the 15th precinct, not the 13th, and there is no longer a 15th precinct in NYC.
The NYPD does not issue Beretta 9 series pistols in any capacity to NYPD officers (detectives, plainclothes). The NYPD also does not issue shotguns to non-tactical units, such as detective squads or patrol.
During a car chase Chen drives down an alley scraping both sides of his car then he and his opponent bang the sides of their cars into each other but there is no sign of any damage to Chen's car even after the bad guys fire machine guns at it.
Before shooting out the tires on the red vehicle, the 2 officers unload dozens of pistol and shotgun rounds towards the approaching vehicle. NYPD does not authorize firing at a moving vehicle when the vehicle alone is being used as a weapon. Also, with pursuing Patrol Cars behind the red vehicle, they were essentially firing at other officers.
During the shootout in the lights store with the Dragons, bullets would have gone through the table that Nick took cover behind hitting him, and the persons involved fired more rounds than their respective weapons could hold.