Factual error: When they launch the F-16's to intercept the Soviet "Backfire" Bomber, the picture shown is of two F-15's. In addition, no F-16's were stationed in Alaska to handle air defense duties, this was handled exclusively by F-15A/C's.
Factual error: At the end of the movie WOPR tries to crack the launch-code using brute force. So far so good. When WOPR finds out one digit of the 10 digit code, the first digit locks and the search goes on with the remaining 9 digits. Then he finds the second one, it locks too and so on. Problem is, brute force doesn't work that way. It would be too easy (26 letters and 10 numbers = only 36 possibilities for one digit). Brute-Force works only "all or nothing", you can't sneak your way to the whole code one by one.
Continuity mistake: Near the end of the movie, the panel has JPE 1704 TKS showing, but when Joshua finds the launch code, CPE 1704 TKS is blinking on the screen.
Continuity mistake: The tour group comes in and they trick the black lady into pressing the red "launch" button that displays the welcome on the screen. Just before she presses it she has a 35 mm camera hanging around her neck, but in the next shot of the group standing in front of the panel her camera is gone.
Factual error: In two different scenes, Matthew Broderick lifts the phone receiver off his modem-once during the scene where it's dialing numbers in Sunnyvale, CA, and again when WOPR keeps calling his phone trying to reconnect. In both cases, the activity on the screen should have disappeared, since lifting the phone off the modem cradle disconnects the signal. Yet the computer somehow manages to keep dialing numbers, or display the running game clock on the simulation, without any interruption.
Factual error: During the part where they're in NORAD and watching all of the Soviet "nukes" hit various bases in the US, a base in northern Maine is listed as, "Loring AFB 43 Bomb Wing." This was a real air force base, but it was the 42nd Bomb Wing that flew B-52s out of Loring. The 43rd Bomb Wing did exist, too, but it was based at Andersen Air Force Base, Guam, in the North Pacific.