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: The family ask 3 so-called ghost experts into the house. After seeing flying objects in the kids' room, they are suitably impressed. But later on, the female expert is sleeping, one of the men is in the kitchen wanting to cook a steak, and the second man has his back to the monitors, his head buried in a crossword puzzle and he has headphones on with music on, so he can't see, hear or see what is going on.
Suggested correction: The only one acting stupid in this scene is the guy at the monitors. They have to eat and sleep sometime; if anything, having two people awake and one asleep at a time is the cautious route. The one guy goes into the kitchen to cook a steak, but the guy at the monitors, despite being told he'll be the only one watching them, doesn't put down his drawing or take off his headphones, depriving him of sight and sound.
Stupidity: The fact that Nolte even gives in to Eddie's demands is ridiculous. Why not just interview him in prison, ask him where to look for certain people, etc, and if it's a dead end, report back and ask for further tips, etc. They had zero problem going to prison and asking Kirkland Smith in the sequel.
Suggested correction: He refused to tell him anything unless Kates takes him out of prison.
Stupidity: A detective who explicitly frequents morgues not being able to tell the difference between a real slashed throat and fake blood spurted on a neck is one thing. When he returns to the room and finds the body missing, instead of becoming alert, drawing his gun, putting his head on a swivel, and warning his friend outside, he slowly walks over to examine the razor and figure out how the magic trick was performed, allowing the killer to ambush and kill him almost comically easily.
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.