Continuity mistake: When Jack tries to get on the bus on the highway, he hits the door window and breaks it with his elbow. Later, when he finally catches up with the bus and gets on from the moving car, the door window is intact. Several times later it is visible, no break. Then later, when the bus is on the freeway, the glass is shown broken again, but in a different pattern.
Continuity mistake: When Dennis Hopper psyches the police chief out by making him think he's on the third floor, the elevator clicks one too many times. The camera shows the numbers: "5, click, 4, click" then it switches to the police chief, during which time you hear another click. It then switches back to the numbers: "3, click." Shouldn't it be on floor 2?
Continuity mistake: When they run onto the roof near the start, there's another trooper behind Harry running onto the roof (only visible in widescreen - in 4:3 it looks like a weird reflection). In the following shot of Keanu Reeves you can see the reflections of Harry and the other guy on the plastic covering the scaffolding. We're led to believe that Harry and Jack should be the only ones up there, as everyone else has a job to do. Aside from those two shots, this third trooper disappears once they start hooking the crane up.
Continuity mistake: Just after the bus driver has been unloaded and Helen tries to get off, Annie shouts "No Helen" at which point Jack turns around and grabs her shoulder to stop her. The shot switches to Dennis Hopper watching TV and then back to the bus where Jack is no longer even close to Helen when the bomb detonates.
Continuity mistake: When the LAPD are making the money drop, one shot from Dennis Hopper's apartment shows a businessman walking past the garbage can with a silver briefcase (just as the garbage man comes), and the same man with the silver briefcase walks past about a minute later in another shot when Keanu Reeves is running towards the bin.