Continuity mistake: When everyone is trying to get Joshua/WOPR to stand down from launching its own missiles, McKittrick's assistant Paul is standing with the rest of the group, but then there is a quick shot of Paul looking at the WOPR and then within seconds Paul is overheard saying "must be caught in a loop" as if he's standing beside everyone again.
Other mistake: When David first logs into the system after finding the right password, it shows a phone # beginning with the prefix 936. The only problem was that earlier when his computer was dialing numbers, he had not gotten to 936 yet. That was the 4th prefix and he only got through the first 3. There is no way he could have dialed that number with his computer program.
Other mistake: When David was having his computer dial all the numbers in Sunnyvale, he pulled up the list of numbers already dialled, and there are numbers with the prefix '936', but before he pulled up the list, when the computer was dialling the numbers, the 936 prefix was on the far right hand side. No numbers with the 936 prefix were dialled yet, so they could not have been on the list.
Continuity mistake: When Matthew Broderick is first at his computer the screen is large and has an external modem on top. Later there is a close up shot of the keyboard and the monitor. At this point the monitor is completely different and much smaller. Then shortly afterwards you can see the larger monitor again with the modem on top (behind Ally Sheedy) while it war dials numbers. Shortly after that, the monitor changes again. You can also see the changes with the color and the "side handles" used for carrying. I counted three different monitors being used.
Factual error: In the first scene with the computer (when Ally Sheedy visits) Matthew Broderick puts the handset on to the modem coupler with the cord toward him, then pushes the button on the modem which is facing him. A shortly while later he is at the computer and he puts the handset backwards with the cord away from him and pushes the button which is still facing towards him. The modem would not have worked properly, since it needs to send and receive through the respective ear and mouth pieces.