When Nicolas is talking with a woman by the phone, she tells him that Nikko Hotel has his credit card. She tells him that the Hotel's phone number is 555-1111, but when he immediately calls the Hotel, he dials another number, totally different than 555-1111.
Nicholas confronts one of CRS's employees at the Zoo trying to find out who is in charge. The employee tells him "This is extremely dangerous." Nicholas replies, "No you don't understand *I'm* extremely dangerous." at which point you can clearly hear his gun being cocked. He then puts the gun to the employee's neck but the gun is not cocked.
In the elevator scene, Nicholas climbs up and grabs the cables with both hands to pull himself up first. Then after he helps Christine pull her up after him, one of his hand's is clean and no grease is on his shirt.
After the pen spills ink on Nicholas' shirt, he goes in the bathroom to try and clean it up. As he leaves the bathroom, he clearly buttons his coat to cover the ink spot, but in the next scene in the restaurant the coat is unbuttoned again.
When Nicolas is watching the film strip, he gets fed up and stands. He looks back and clearly is standing in the way of the film's projection onto the screen, but when the screen is shown there is no shadow.
When Nicholas is at work, the secretary walks in to tell him his ex-wife is on the phone. The secretary then wishes him a happy birthday. We can assume she is calling to wish him the same. But later that night when his ex calls again, Nicholas says to her "You almost missed [my birthday] this year!"
When Van Orton and 'Christine' leave from his office in separate taxis, Christine's cab stops just off-camera - the reflection of the brake lights from the cab can clearly be seen in the bumper of the remaining taxi.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
Near the end of the movie, Nicholas, distraught over what he believed to be the death of his brother by his own hand, calmly strolls to the edge of the buildings roof and walks off. The problem with this scenario is that in order for the "game" to play itself out to completion, he had to leap from a very specific point on the rooftop. The camera shot from within the ceiling as he crashes through the glass shows that his downward path led through a very narrow space between the metal I-beams and other structures. A deviation of a mere few feet in any direction more than likely would have resulted in Nicholas' death. Since there were no erected barriers on the roof or gaming personnel guiding him to the exact spot for him to fall from in order for him to safely descend through the glass ceiling, how could the games planners have known precisely where he would choose to leap? However, after the jump, a character says that it was where he was meant to throw Michael Douglas off the roof, hence he would have landed on the airbag safely.