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)
Revealing mistake: Watch closely as Phoenix is about to fight the cops near the computer kiosk: the same two people wearing white robes pass behind the officer with the hand-held computer twice. (00:25:30)
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)
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)
Plot hole: Even if the 30 bus passengers that were already dead had been burned up in the explosion of the building their bodies would still have been autopsied after the fact, thus proving that Phoenix had killed them beforehand and vindicated Spartan.
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.
Character mistake: When the alarms go off in the police station indicating the code 187 all the police officers are confused as to what is going on since they know nothing of MDKs. Zack Lamb should have already known what the code meant, yet he never says anything and just waits for everyone to figure it out.
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.
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)
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)
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)
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)
Continuity 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)