3.72 : The Mark of Gideon.
The one with a duplicate Enterprise.
Let's start with the big questions: How and why did the Gideons create a replica of the Enterprise perfect enough to fool Captain Kirk completely? Kirk knows his ship inside and out (he says so!) Yet Kirk says that he has searched every area of the mock-up, and even Spock says that the copy is an exact duplicate of the real Enterprise.
Where would Gideon, a non-aligned world, get exact specifications of a Starfleet vessel? How would they know about the alterations Scotty had made, the personalised decor, and the familar functional sounds?
If room to live is such a premium on Gideon, (with people willing to kill to get a moments privacy) then why go to all the trouble - and space - to build this rather large mock-up, which will be used for a relatively short time? (Presumably they didn't expect to keep Kirk there for ever.) One suggestion is that it could have become an amusement park, but surely there would be a better way to get Kirk to stay.
After going to all that trouble, wouldn't they make sure the population stayed clear of the imitation spaceship? Allowing them to look in through the windows does kinda spoil the illusion.
Finally, why does Kirk believe Odona? He takes her word that his crew have vanished, yet she can provide no explanation to why, or how she got there. He does not interrogate her with any severity.
Scotty is called a "very excitable repair-man".
Spock almost gets emotional with the stubborn Starfleet bureaucracy.