When you get into a police car you receive a shotgun. The gun is strangely a Remington "Folding Stock" Shotgun, in reality police officers carry a 12 Gauge Shotgun in their cars and have the ammo separated from the gun, not already loaded.
In the game, the LCPD police cars are black and white. They were supposed to be blue to represent the NYPD's older styled vehicles, but because the game was released shortly after the September 11th attacks, Rockstar canceled the blue paint scheme and made them black and white.
When you go up to a random car and start shooting at it, notice that there are no cracks in the windshield or bullet holes in the doors or hood. Its as if the entire car were bullet proof including the tires.
If the character severely damages the back of his car such as removing the trunk or reversing into another car or wall, notice that the tail lights still work normally regardless of how much damage is done.
When the player enters the airport notice that there is a fire station with a "street version" fire truck. That is strange because in reality airports have their own fire trucks which are massive size trucks with six huge tires, not the ones that you see on city streets.
Although of insignificance, during the police convoy scene, it is clear that there are at least 4 police officers in total. (At least one driver in the police cruiser and one driver of the van with two officers in the back on the van.) Once the fictional "patriot" SUV stops the police cruiser, only two officers exit their vehicles. The driver of the police cruiser and the police van, although animated, did not make an attempt aid their fellow officers or to continue driving forward. This is very strange, although this realism would strongly tamper with the actual introduction. Furthermore, if you look inside the Patriot when it swerves in front of the police cruiser there's no one actually driving it, this is true for the white Rumpo van that the two Colombians emerge from.
Whenever a gang member attacks the player or a random NPC and the police are nearby, the police cars and officers won't react or go after them. Instead, the police will only go after the player even when they retaliate to a gang member attack. The only time the police reacts to an NPC attack is when they are caught in the crossfire.
When the player has a wanted star and is being chased by a police officer on foot, the player can escape by climbing into a car, closing the door behind them and driving away. However, the police officer can open the player's door while the player starts driving; rather than reacting to the vehicle in motion, the officer literally stands in place and opens the door as though the car was perfectly still.