Revealing mistake: When Arnold horseback rides towards the hotel, Tom Arnold's van skids and you can see that he is a stuntman with a very cheap latex mask to resemble Tom.
Continuity mistake: When Harry gets in the Harrier, the aircraft's left forward nozzle is directed aft. In the next shot, the right forward nozzle is aimed down. The nozzles cannot be aimed in different directions. Additionally, the nozzles are aimed aft and down in subsequent shots of the same scene.
Continuity mistake: When Helen is on the couch with Simon, objects on the tables move around. Most notably, the books on the end table change position as well as which one is on top when the spies break in.
Continuity mistake: When Salim Abu Aziz slides through the intersection on the motorcycle, as he's being boxed in and before going into the hotel, the stopped cars change between shots. You see him stop near a white car with round, pop-up headlights, then in the next shot it's a different white car with inset square headlights. Then back to the first white car.
Continuity mistake: In the first scene in the Omega Sector debriefing room, after Francis leaves, the people in the background change too quickly between shots. Most noticeable, the man standing next the seated woman at the computer is gone and a woman from nowhere is in his place.
Continuity mistake: In the scene where Harry discovers Helen is having an affair and he's walking across the road. Between the wide and close up shots his wedding ring appears in the close up shots and disappears in the wide shots.
Continuity mistake: When Simon pees himself, Albert's hat keeps changing the way it's tucked on his head in every single angle until he gets to the van. Watch for the right side of his temple and cheek. (01:14:25)
Continuity mistake: Harry leaves the pack of cigarettes 15 cm away from the sink, in the close-up it's right next to it. (00:29:40)
Continuity mistake: When Harry dances the Tango with Juno there's a wide shot of the place, in the immediate close-up two guards appear out of nowhere behind Harry.
Continuity mistake: The position of the champagne bottle holder and the next chair changes between shots. When Michelle enters the room and the camera is placed in the bedroom, the bottle holder stands between (and somewhat behind) the chair and the window wall. When Michelle approaches the table (camera is now Michelle) the chair is between the bottle holder and the window wall. Later, at the end of the scene this changes again, depending on where the camera is. (01:19:50)
Revealing mistake: When Harry confesses to Helen that he's a spy she punches him and knocks him down. When he falls one can notice it's Arnie's stunt double.
Continuity mistake: After Juno Skinner has killed her limo driver, the limo speeds out of control. There are two champagne glasses in the cup holders next to Juno, but both glasses disappear and reappear between shots while Juno and Helen are fighting each other. With the limo speeding across the bridge, it doesn't make sense that Juno's gun stays on the roof for a while. The gun should have slid off the roof when the limo banged into the guard rails. It doesn't fall off until after the limo has passed through the flaming truck wreck.
Continuity mistake: During the scene when Arnold is taking off in the harrier jet, the pilots hide behind a squad car. One pilot is holding his sunglasses. It switches angles and he no longer has sunglasses on. Then his hand moves and they appear as if they had fallen off and he was grabbing them. A few frames later they disappear again. If you look closely, it was obvious they were CGI'd in during editing.
Continuity mistake: When Harry, Helen and Juno are in the private jet, the amount of lipstick smear on his face changes between shots.
Continuity mistake: After the Swiss scene, Harry, Albert and Faisil are in the office. Albert talks about the Chinese woman and the dozens screens behind are broadcasting news reports. When they walk away, a mere frame later, the images on the screens surrounding are completely different, now broadcasting satellite images and computer texts. (00:21:35)
Factual error: When Harry is being interrogated by Samir, he gets drugged with something he refers to as sodium amytal (amobarbital) which is a treatment for insomnia and not a truth agent as Harry refers to it as. (01:33:46)
Suggested correction: To date, I don't believe there are any reliable "truth serums." Substances/barbituates used as so-called "truth serums" basically slow down messages to the brain, thereby (in theory) making it more difficult for some people to lie because lying requires thinking/ concentration. Sodium Amytal may still be referred to as a "truth serum", but is no longer used for this purpose. (Some people developed false memories). You are correct, however, that it may be used for insomnia because it is a sedative.
Other mistake: Harry commandeers one of the AV8-A's to go to save his daughter, and makes a clumsy vertical takeoff (where he bumps the police cars, etc). The reality is that, besides the deafening noise, the AV8-A generates a strong down wash when it takes off vertically which would have blown all the people on the bridge (and even some of the cars) in all directions. A few seconds later there is a cut to a real AV8-A vertical takeoff over water where we can see the effect of a real down wash on the water's surface. (02:02:20)
Other mistake: When Harry fires the Harrier's Sidewinder missile with the lead terrorist attached to it, he has to switch on the "master arm switch". That switch would have already have been enabled in order to fire the Harrier's gun.
Audio problem: Harry and Gib pull over to the side of the road, and Harry yells "Give me the goddamn page!" and smashes the SUV window. Harry yells this line during a shot transition, and in the end of the first shot ("Give me-") his mouth isn't moving, yet in the next shot ("-the goddamn page!") his mouth IS moving. (00:57:05)
Revealing mistake: In the scene at the beginning of the film where Faisal is in the van and decrypting the files, he says "Yeah, I got your password," and then the camera swings down to show his fingers on the keyboard, pressing repeatedly on the same set of keys and looking rather unrealistic. (00:07:30)