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.
Factual error: It is long-established in Star Trek canon that onboard diagnostics can detect any animate intruders on Federation vessels. Any living thing that exists upon a Federation vessel can be identified, and its location specifically noted on Federation property. How is it, then, that there are rats aboard the Regula I space station (as observed by Doctor McCoy) that haven't been eradicated?