In case you forgot: A murder mystery with Scotty at center stage (spoiler: he's innocent) leads to Jack the Ripper taking over the Enterprise's computers. McCoy drugs everyone up, Spock gets Jack the Ripper out of the computer by asking it to calculate pi to the last digit, and then they beam it into space.
A creepy alien entity taking over the ship's computer is a cool idea, especially as the entity we're talking about is a disembodied entity and not some human with godlike psychic powers that, at the end of the day, is still within the realm of our understanding. Sure, it comes down as another "man versus COM-PYOO-TOR" trope, as we've seen in other episodes on this list and will continue to see, but the idea actually works pretty well for me because this one doesn't preach the inherent superiority of humans when it comes to whatever; it's just about troubleshooting what is understood to be a necessary and overall beneficial piece of technology.
As for murder mystery in your science fiction, you can take it or leave it. Personally, I'll take it—whodunnit habits die hard—but this is not the world's best genre crossover episode. (That award goes, for TOS, to "The Conscience of a King.") Heck, even "Court Martial," which even harps on the "man versus COM-PYOO-TOR" theme as well, has a much more coherent and organized story while weaving in elements of the classic court procedural.
Coherence. Organization. Those are really the biggest problems with this episode. It's a human centipede of a story. Like Zack Handlen wrote over at The A.V. Club,
[i]t's like Bloch wrote the first couple acts, went out for some drinks, and came back six months later and finished the script without bothering to reread what he'd already got down.Because by the second half or so, we are out of the Space Murder, She Space-Wrote field entirely and back into solid Monster of the Week territory. Both are solid ideas (murder! in! space! and the ghost in the machine) and both really should have had their full 50 minutes of treatment.