More people should be overseeing such a dangerous and complex system
Keep a human in the loop or use another non-software fail-safe
Dr. Falken's creation, Joshua, was in charge of launching nuclear missiles in the event that were need to retaliate against attackers. When the general tried to stop the launch, he was locked out of the system. Being unable to stop a nuclear launch if one is initiated by mistake is a massive software bug. There should've been many knowledgeable computer scientists working on this software to make absolute certain that nothing like this could ever happen and that there were no backdoors that a hacker could easily use to break in. An emergency kill switch independent of software working would've gone a long way to preventing this situation.
Originally, there were human missile silo operators that had to turn keys at the same time in order to launch. When they were replaced, NORAD lost an important fail-safe in the system. Without them, Joshua has the ability to take a launch code and then launch the missiles on its own. Any number of bugs in different areas of the code could turn an innocent mistake into a disaster. However, no one expected Joshua to start brute-forcing the launch codes until it found a match. At was at this point that they should've been able to use an emergency shutoff to stop Joshua in its tracks.
Lightman learns an important lesson that he should not break in to unknown systems. The events of the movie were set into motion because Lightman was trying to illegally dial into the system of a game company to play new games before their release. It is important that we all use computers responsibly to prevent unintended negative consequences.
[1] YouTube, WarGames, 6 Jan. 2020, www.youtube.com/watch?v=HNLQ-O-Qx3Y&t=1779s&ab_channel=YouTubeMovies (20 Sept. 2021)