Early on Chev is driving a Buick Riviera featuring license plates with light letters/numbers on a dark background, similar to the California 1963 issue. When he ditches the car after the shopping mall crash the car clearly has a different front plate.
Throughout the movie, references to "Chinese" items and characters are continually made. "Don Kim" is said to be Chinese though Kim is traditionally a Korean name. In the "Chinatown" section of the movie, when the school girls are interviewed for the news, they are speaking Korean. Also in the warehouse the workers also speak Korean. A hint that this is a purposeful "mistake" by the director/writer is made when, in the hospital, a page is heard calling for anyone who can speak Korean.
When Doc Miles is consulting Chev on epinephrine while Chev is driving a taxi, he says that epinephrine comes in 10mg syringes. The syringe that is shown later and that is actually used to store epinephrine in places like ER contains 1ml of epinephrine. 1mg/10ml epinephrine solution is usually used, so Doc is clearly wrong.
In the beginning, Chev wakes up to his cell phone ringing. When he finishes watching the DVD and rushes out the door, his cell is ringing again, yet when the phone is shown, it only says "1 unanswered call".
Throughout the car chase, the yellow Volkswagen convertible (which somehow can outrun two larger far more powerful cars) is shot at close range, multiple times, by thugs with automatic weapons. While the glass is shattered, and reappears several times, the body itself never shows any signs of having been hit by a bullet.
When Chev and Carlito meet in the pool, we see them swimming in the middle. In the next shot Carlito is very close to the edge, and in the next one they are swimming in the middle again. This changes several times.
When Chev is running through the hospital corridor, he tucks his handgun under his left armpit. In the next shot, when he jumps off the wall to get around some people in his way, there is no gun in sight on him. Since he is wearing only a loose hospital gown, it would be impossible for the gun to be secured anywhere but in his hands or armpits. In the next shot, he has the gun in his right hand.
When Chev's doctor tells him to find some epinephrine at the hospital, he tells Chev the drug is stored in syringes (it is stored this way, at least in ERs so it is ready for immediate use). When Chev finally gets the nurse to hand him the drug from the crash cart, he is handed empty syringes and a vial of the medicine.
During the convertible chase, Chev fires out the passenger window at one of the cars. A moment later, the car swings left around a curve, and the passenger window is up. After the second car wrecks, the passenger window is down again.
When Chev pulls his semi-automatic handgun on the black guy in the beginning you can see a small pin on the rear of the handgun. This is a feature on the Springfield XD that allows you to tell if the handgun has been charged in this position it is. In the next shots you cannot see the pin meaning the pistol is not charged.
Towards the end of the movie, when Chev, Verona, Carlito and company are on the rooftop of the hotel, shortly after Chev and Carlito have their conversation about the insulin pump, Verona drinks and clearly finishes his glass of champagne. In the next shot, his glass still has a good amount of champagne in it, which he drinks in one gulp again seconds later, after standing up and point his gun and threatening Chev.
When Chev Chelios is projected into the elevator he fires a shot at the police and the slide doesn't return, indicating the magazine is empty. When the shot cuts to another angle of Chev, the gun the slide is returned forward.
When Chev's doctor calls to check on the effects of the adrenaline, the camera shows an aircraft that the doctor is supposedly on board. The aircraft they show is actually a Singapore Airlines Mega Ark which is a cargo aircraft and has no commercial passengers. You can tell this is a mega ark by the distinctive insignia on the bottom of the nosecone.
When Chev steals the LAPD motorcycle it clearly has a diamond E (exempt) license plate. Diamond E plates are for state vehicles only, county and municipal vehicles are issued exempt tags with an E inside an octagon.
In the scene when he is running down the street, after he leaves the hospital, he passes two cars parked on the left: a Del Sol and a Mustang). Their images are reversed making each car appear RHD, and their license plates backwards.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
In the end of the movie Chev is falling from the helicopter and calls his girlfriend, Eve, using his cellphone. When you hear his voice on her answering machine, it is perfectly clear. Normally, this wouldn't be possible, as the extreme speed would make any speech inaudible due to the wind. However, it is revealed in Crank : High Voltage that this was merely the way Chev imagined the message would sound when she would play it back, as Chev asks her in the second film "didn't you get my message?" and we cut to the answering machine, playing nothing but the sound of very heavy wind with an inaudible voice muffled in the distance.
It seems that having fallen from a helicopter he would not have had enough time to do all the things he's done (fighting, dialing, leaving a message, etc.). But, Chev's total falling time was 60-90 seconds (depends on how you consider the slow motion and the fight in the air editing) which means that the helicopter's altitude was 3100-4800 meters. This is well inside the service ceiling of Eurocopter AS350 Ecureuil Helicopter used in this scene (5100 meters). So, theoretically, there was enough time during the fall.