Continuity mistake: When Phoenix throws Spartan over the bonnet of the red car in the museum, Spartan lands in a puddle that soaks his hair. In the next few shots, the hair keeps changing from being soaked to being dry. (00:50:15)
Factual error: During the fight in the museum, Spartan gets three shots out of a shotgun which only holds two shells. (00:48:35)
Plot hole: When Spartan jumps through the window in the excavation scene of the museum, he crashes into a room with bottles of drink on the shelves. Surely this room too would have been filled in and the window smashed during the earthquake, and the museum wouldn't have bothered to excavate it as it can't be seen from above due to the blanked out window. So what is that room doing there? (00:49:20)
Continuity mistake: When Phoenix blows up the door sealing the Armory, it is just about the size of a normal door, but when he runs through it to escape into the main hall, the door is four times larger. (00:47:40 - 00:48:40)
Suggested correction: Phoenix didn't exit through the door of the armory same as where he entered. As he says, "I've been dreaming about killing you for forty years", he shoots the large window that's to his right, near where the cannons are. This is where he exits, which is why it looks bigger.
Other mistake: It seems curious that the museum, even in the weapons display, would have functional firearms and LIVE munitions of any sort, even if no one would be interested in ever taking and using them.
BlathropRevealing mistake: When Cocteau's corpse is thrown into the fireplace, you can see that it is a dummy due to the fact the the hair is longer and shaggy. (01:38:05)
Phaneron
Continuity mistake: When an employee wipes the frost of the date display in 2032, it says that it's August 3rd. However, after the 187 alert, when Huxley accesses the parole hearings for the cryoprison later that very same day, the computer says that it's August 4th.
Other mistake: When Simon Phoenix kicks through the windshield of the police car during his first fight with the SAPD, the windshield easily breaks into several large segments, as opposed to spider-webbing like real windshields made from safety glass do. Glass that would completely shatter and collapse into the car from a simple kick would be completely unsafe and illogical for a society that's supposed to be more technologically advanced than ours.
Phaneron 
Continuity mistake: During the glass floor shootout at the museum Spartan shoots a light that falls through the glass. Right after Spartan shoots the light it goes dark but the close up of the light falling and hitting the floor shows the light to be still lit. (00:49:05)
Audio problem: After John Spartan crashes through the police station sign he says, "All I need is a needle and a thread." But when the camera is behind him and he says the line, "I really didn't say that, did I?" his mouth doesn't move when his face is in frame. (01:35:35)
Continuity mistake: When Phoenix first gets out he makes his way to a computer and the police come to arrest him. Phoenix takes one of the policeman and pushes his head through the side glass pane and walks away to fight the other officers, but when Phoenix goes back over to the computer the glass is not broken. (00:26:50 - 00:27:40)
MCKDAudio problem: In the European version, Taco Bell is replaced by Pizza Hut, however, when Huxley says to John Spartan that they're going to Pizza Hut, her lips say "Taco Bell". (00:57:00)
Factual error: Simon Phoenix uses the warden's removed eye to escape from the cryoprison. The eye is on a pen, and since the retina includes the back portion of the eye, the pen's nib would have not only destroyed the shape of the retina, but blocked the scanner from reading the complete retina as well. There's no way the retinal scanner would have let him pass. (00:18:45)
Suggested correction: This is a fictional device, it can work in any way shown as long as it is in consistent manner.
This is not a valid correction. First, stating it's a fictional device and can do whatever it wants is used incorrectly too often. Second, retinal scans are not fictional. Now if the machine had simply said "scan" or "eye scan" complete, one could argue we don't know how it worked.
Bishop73Revealing mistake: The cables Spartan slices in order to bring down the parasol, have quickreleases on them so that they snap in the right place. This is best visible with the second one. (01:01:50)
Friso94Continuity mistake: When Spartan is initially frozen in the cyro-liquid, air bubbles and ripples are in the ice around his mouth. Any following shot of him in the ice block shows no bubbles or ripples. (00:10:15)
Factual error: In the scene where Wesley Snipes has supposedly poured gasoline all over the floor, he lights a torch and holds it inches from the floor threatening to light it if Sylvester Stallone comes any closer. Had it been actual gasoline, with that much of it the fumes would have exploded as soon as he lit the torch. It's the fumes that are explosive, not the liquid.
Continuity mistake: When Spartan and Huxley go to Raymond Cockto's place, Spartan shoots all of the monitors with a silver gun, yet when Spartan points the gun at Cockto's head, which we see on the surviving monitor, it's a black gun. (01:18:25)
Mark CussContinuity mistake: When Phoenix is fighting the police at the kiosk, he knocks the sunglasses off of one officer, but in the next shot the glasses are back when the cop is knocked out. (00:27:00)
Character mistake: In the scene where John Spartan goes into the sewers, he has a conversation with a Spanish-speaking woman. At the end of their conversation the woman says "Gracias" (correct Spanish) to which Spartan replies "Prego", which is Italian. Up until that point Spartan spoke perfect Spanish. (01:23:30)
fatpigsittinonacouch1Continuity mistake: In Cockto's office, Phoenix gets up from the chair behind the desk, turning it clockwise to get up. But, when he's at the window, reciting a couple of cities, the chair is turned to squarely face the desk.
