Revealing mistake: In the first meeting with the Director of the FBI, you can see some of the latex is peeling off the Russian Major's burn, just over the right eyebrow there's a small flap of it. (00:13:15)
Continuity mistake: When Bruce Willis is driving his car to the abandoned warehouse to get the "gun" to commit the assassination on the first lady, the vehicle does not have a license plate... You can see that it is missing, plain as day... In the next scene, he pulls a switch, removing a once non-existent plate and replacing it with another. (00:45:50 - 00:49:15)
Suggested correction: These scenes take place at least half a day apart. The shot where he has no licence plate is during mid day. There is then an unknown time laps to night time after he's left that area and hanging out at a restaurant eating. There is plenty of time between these moments for him to have stopped and attached a licence plate to his van. Reasons for this happening are never shown or stated but it's not unreasonable to think that he could have removed the plates to go to one location and then added plates to go somewhere else in one of his ways of masking his movements. In fact, when he's going into the parking garage to spray off the paint on his van, he even changes out his licence plate at that point showing that he has multiple. This is just speculation but there's enough backing that this can not be considered a definitive mistake.
Continuity mistake: Toward the end of the movie, the assassin (Willis) fatally shoots the female Russian agent (Venora). As Willis is advising Venora that she will die within twenty minutes, he draws a picture on her cheek with her own blood (a grim pictogram of a love heart). When Gere arrives on the scene a few minutes later, there is no sign of blood anywhere on Venora's face. Obviously, the authorities would not have washed away such a vital clue. Neither would emergency personnel have transferred the victim from the floor where she was lying, onto the living room couch; rather, they would have put her on the ambulance stretcher. (01:26:00 - 01:27:15)
Suggested correction: There is several minutes taking place between these two shots, and Koslova is alive during that time. She was on the floor when the Jackal draws it on her face, and then when Declan is with her, she's on the couch. It is likely that the paramedics moved her to the couch, or she may have moved herself. We don't know how much time lapsed between her conversation with The Jackal and when the medical team arrived. It's very probable that she wiped it off herself. She had blood on her face drawn in a picture by a sadistic killer she hates that just killed two of her friends and is now leaving her to a slow painful death. If I were in that situation and that guy drew a heart on my face with my own blood, I'd wipe it off too. You can still see a faint bit of red on her cheek where it was.
Revealing mistake: In the scene towards the end, where Declan has chased the Jackal back onto the subway platform, and has just followed on himself, behind him you see a man (possibly a cop) running to get out of the way of the guns, but just before going out of shot, he stops running and just casually 'strolls' to the edge of the set (some kind of small booth or shop on the platform). (01:50:55)
Suggested correction: This doesn't really reveal any mistake. I see the guy he runs into it and then slows down as he looks back. There's not really much else place to go and he just saw that Declan wasn't shooting any of them, that the previous guy, The Jackal, was the one shooting the cop. There doesn't appear to be anything wrong with how this man acted as he went into that booth.
I watched the scene and he's running out of fear along with everyone else and the just stops running, as if he thinks he's off camera, and the starts to walk, but he never turns around. Everyone else is ducking if they're not running. It would not be a natural reaction in that situation, especially since people were still screaming.