Stupidity: Reliant's prefix code is 16309. This code prevents an enemy ship from ordering a friendly ship to lower its shields or something similar. Five digits with no symbols. We know that symbols and letters aren't used since Spock uses a 10 digit set of switches to input the code. This is ludicrous. In 2016, a high powered server could crack a 6 digit password in approximately 0.0224 seconds (at 100 billion guesses/second). Any starship computer would have to far more processing power then a 2016 server. The prefix code protecting a starship from cyber attack would have to be insanely complex in order to be useful.
Stupidity: As much as I love this movie, this has always bothered me. When discovered on Regula Station, Chekov literally tells Kirk, McCoy and the others that Khan put creatures in their bodies to make them, "Say lies, do things." It doesn't seem to occur to McCoy or Kirk to scan them to see if the creatures are still there.
Stupidity: Scotty takes his mortally wounded nephew to the bridge before taking him to sickbay.
Suggested correction: Keep in mind the era that this movie was made in. This movie was made before PCs really existed. Computers at this time were typically huge devices or box like containers. Their data storage capacity was minuscule and there certainly wasn't any form of AI logic programs built to "hack" passwords. I know this movie is about space and set in the future but there's a lot of stuff in Star Trek movies that based on our technology or development currently, we would expect something bigger, smarter, etc. We still have problems today with people using archaic password structures like 1.2.3.4. or actually using the word password for/in their password. Back in '81-'82, I'm sure that most people would not have thought about codes being hacked. This is not to mention that in many movies, which I don't know if there is a specific reason for using 16309, codes, passwords, numbers for addresses/apt#/room#/etc and other info frequently come about as tribute, honoring, or coming from something in the lives of a film's director/producer/actor/etc! So sure with today's technology, which could have been accomplished more than 10 years ago as well, using a single string of numbers as security measures for anything is foolish and can be hack by a self running password-like cracker program... But they made this "code" back in the very early 80s when computer hacking was barely unconscionable (MAYBE) so unless these #s were a tribute or to honor something, I'm pretty sure no one was even thinking of hacking back then... We all aware of today... all about the hacking threats and YET we still have people using 1.2.3.4., the word password, or other horrible predictable password choices that can easily be broken by a password cracking program... And we know that there's a huge hacking threat requiring strong security measures but don't do so while back then, there was little awareness of the threats of hacking much less the concept of hacking altogether.
OR... in this future they have limited the number of password attempts to one a day and the ship automatically goes to red alert after a failed attempt until the right code is entered. That way it would take 7,327 years or so to try all the codes with the crew on notice and plenty of time to address the threat.