Plot hole: While planting the suicide gear in the bathroom before Buckley comes in, Cooper tells Josh to tie the rope into a noose as they go to hide in the shower. Josh replies that he doesn't even know how to tie a noose. He must be a quick study, because in the 45 seconds or so that it would have taken Buckley to relieve himself and wash his hands, Josh has tied a perfect noose.
Audio problem: When the crowd is gathering around Cliff after he falls from the balcony, you can hear a lot of the same background dialog being looped over and over. Some of the easier ones to spot are guys yelling "Right there, man." and "Where is it?" and a girl yelling "Stop." Those three can be heard distinctly at least three times.
Continuity mistake: When Josh and Cooper break into the Mental Health Facility, we see the entire pane of glass broken out and falling towards the camera. In the next shot, we still hear Cooper breaking away glass, and when Josh flips the window up, broken glass still remains in the frame, even though the whole pane was gone.
Continuity mistake: When Josh is on the phone with his mom and Cooper interrupts, the door and hallway change. When Cooper first barges in, the door appears to be very light in color, and a door and light fixture are visible in the hall. Less than a minute later, when Josh opens the door, the door is a much darker wood color, the door across the hall has been replaced with a column and molding, and the light fixture has moved quite a bit from where it was.
Plot hole: In his mad dash from the security guard at the Mental Health Facility, Cooper drops about 90% of the file folders he had taken. Yet he somehow manages to hold onto the files for the main people they were photographing earlier in the film. You can argue that he guarded those files better, but then why bother grabbing so many "expendable" files in the first place? It just seems like a cheap plot device.
Audio problem: In the high speed chase scene, Cliff pulls a gun out of the glove box and fires several rounds at the police, which showed a bright muzzle flash. We hear Cliff fire another barrage of shots out the window, but he is not pulling the trigger, and there is no muzzle flash.
Continuity mistake: When Cooper is getting pitchers at the bar, his jacket and shirt are closed and he has his wallet in his left hand. The skeptical bartender asks what is on his shirt, and when the shot changes, the jacket and shirt are now open, revealing a college logo on the shirt underneath. Cooper quickly closes the jacket with his empty left hand, without appearing to set his wallet down or put it away.