I voted for The Changeling, for some of the same reasons I voted for Alternative Factor in season 1, matters of scale. I sometimes think that some of the writers either didn't realize what they were writing within the constraints of the larger background setting or maybe Fontana/Roddenberry were off that time with their script editing, but the results really skew everything for me.
From Alternative Factor: You may not be aware of its scope. It occurred in every quadrant of the galaxy and far beyond.
Then The Changeling:
SPOCK: An extremely powerful bolt of energy, Captain.
KIRK: Full power to the shields, Mister Scott.
SCOTT: Giving them all we got.
KIRK: All hands, Red Alert. Phaser banks stand by. Photon torpedoes to Condition Red, Condition Red.
(The viewscreen fills with a ball of bright light.)
SULU: It's going to hit.
(Everyone gets thrown around a lot, and the lights go out for a short while.)
SCOTT: Shields still holding, sir.
KIRK: Good.
SPOCK: Temporarily, Captain. Our shields absorbed energy equivalent to ninety of our photon torpedoes.
KIRK: Ninety?
SPOCK: I may add, the energy used repulsing this first attack reduced our shielding power twenty percent.
UHURA: First attack, sir?
KIRK: I think we can expect others, Lieutenant.
SPOCK: We can resist three more such attacks. The fourth will shatter our shields completely.
KIRK: Mister Spock, pinpoint the source. Mister Sulu, evasive manoeuvres.
SULU: Aye, sir.
KIRK: Lieutenant, contact Starfleet Command. Patch in my log. Tell them what has happened. Tell them the entire Malurian race seems to have been destroyed by an unknown agency, and that we are under attack by an unidentified force.
(Another ball of light is on the viewscreen)
KIRK: Helmsmen, I said evasive manoeuvres.
SULU: We're losing power, sir.
KIRK: Scotty?
SCOTT: I'm having to divert the warp engine power into the shields, sir, if you want the protection.
KIRK: Mister Spock, speed of those bolts.
SPOCK: Approximately warp fifteen, Captain.
KIRK: Then we can't out run them. Good, Scotty. You're doing the right thing. (another hit) Source, Spock.
SPOCK: Unknown, Captain. Nothing within sensor range. (a third bolt approaching) Something now, Captain. Very small. Bearing one two three degrees, mark one eight. Range ninety thousand kilometres.
KIRK: That's our target, Mister Sulu. Prepare photon torpedo.
(The third bolt hits)
SCOTT: Shields still holding, sir, but the drain on the engines is reaching the critical point. Ach, we lost warp manoeuvreing power. Switching to impulse.
SULU: Photon torpedoes armed, sir.
KIRK: Has the target changed location, Mister Spock?
SPOCK: No, sir. Holding steady.
KIRK: Ready photon torpedo number two, Mister Sulu.
SULU: Ready, sir.
KIRK: Fire.
SULU: Torpedo away. (a pause, then a flash) Direct hit.
SPOCK: No effect. Target absorbed full energy of our torpedo.
KIRK: Absorbed it? There must be damage to your instruments, Spock .
SPOCK: They are in good working order, Captain.
KIRK: But what could have absorbed that much energy and survived?
Um, how about you, yourself, several times over just now? Spock clearly says the equivalent of 90 torpedoes, only reduced their shields 20% and didn't even do those things that happen when the shields get hit too hard almost any other time. Plus this box just wiped out a 4 billion strong population of the solar system. What kind of probe is that? What do these people's actual ships have for firepower?
I also don't like how it casually kills Scotty but then reanimates him. I even more don't like how Uhura's mind is completely blanked but the can reeducate her in a week even though she's reading a first grade reader. That whole scene is supposed to be a joke but it falls completely flat. Either fix the line to say the knowledge wasn't completely wiped out and they can rehabilitate her or not make it like Uhura only knows a week's worth of stuff. I don't believe that this is what they necessarily meant but it seems to me it's like, "it's just Uhura, anybody can be that smart in a week." coupled with the conflicting mass of emotions is just a woman is really demeaning like no other episode.
The machine is magically powerful and Kirk keeps feeding it guards, none of whom are fixed like Scotty.
And I don't believe that it's a life form that can be mind melded with. The scene itself is actually a high point of the episode, very well acted by Leondard Nimoy and a box, but I don't accept the premise of it. I can believe Vulcan mental abilities but extending it to a machine is just wrong, otherwise why doesn't Spock fix the Enterprise by mind melding with the computer or M-5 or Landru any other manner of computer problems.
I vote that this is my least favorite episode tied with And the Children Will Lead.
Also in my bottom 7 (I don't have a full 10 least favorites) is The Apple. I don't mind most of the episode but it's really bad when Mr. Spock can't explain basic biology in a simple logical manner because he's too embarrassed. That really kills this. There's other stuff, but none of it is too bad, but not too good either.
I can't think of any other season 2 problems. I will mention that I used to not like Omega Glory but BillJ and some of the other posters changed my mind on that one and I accept the ending as a kind of "shorthand" for what they are trying to say. So than it being rather literally the USA flag, it's just their equivalent of said flag, and Constitution and Pledge and so on. Why reinvent the wheel for 6 minutes of television? So looking through that lens it's a pretty good episode and a very good use of the prime directive being mentioned.