When Richards, Weiss and Laughlin are sent through the rocket cage tunnel at the beginning of the game show, there is a camera angle that obviously shows the rockets to be going in tandem (one tunnel). This cannot be the case as when Richards hits the safety net at the bottom, he would almost immediately be rear ended by the following rocket (possibly ending Richards game before it had begun).
When Richards is fighting Fireball, he throws several 55 gal barrels at him. The barrels he picks up are made of lightweight polyethylene; however in the following shot, they have been replaced by much heavier steel drums.
At 15 minutes into the movie, when Killian gets out of his limo at the ICS building, he opens his own door fully, with nobody else in the shot, and then the camera angle changes to see a security guard holding it open for him.
During the battle with Buzzsaw and Dynamo the camera changes to the stalker locker room and shows Fireball sitting with a woman in silver and a woman in blue and Capt. Freedom in the background. Later in the scene it shows Capt. Freedom where Fireball was sitting with the two women. But the third time, it shows Fireball back with the two women and Capt. Freedom back in the same position in the background he was in the first shot.
During the aerial attack on Bakersfield, the helicopter's computer shows the Bakersfield coordinates as Lat 45.04 N, Long 119.06 W. These coordinates are actually in the area of Umatilla National Forest of northeastern Oregon, just west of the 395 near Dale. Bakersfield, California is actually Lat 35.37 N, Long 119.02 W. Someone might have typo'd the 35 to 45, but even then, the coordinates are south of the Maricopa Highway, on Snapp Road!
When Richards kills Fireball, he does this near the corpses of last year's winners, however at TV time the crowd doesn't know this, as they can't see the dog tags around their necks, and the TV crew could easily have muted the transmission later. When Mick's film at the end shows the crowd who the bodies belong to, they show surprise. This is because they realize Killian has been lying to them.
Ben Richards uses Amber's pass (it works as a passport) at the airport and the guard doesn't question why he's using her card (plus he doesn't have one, and due to laziness from the officer they manage to breach security)
Early in the movie a commercial for "The Running Man" is shown. All of the scenes in the ads are clips from the "live" show featuring Ben Richards which obviously could not have been shot yet as the ad predates the show.
The goof item below may give away important plot points.
Fireball's death is captured on the show but the moments earlier when Amber discovered that the three "pardoned" prisoners were dead apparently weren't filmed even though the show is broadcast live - very convenient for a show that tends to hide the truth.