Watching the episode, I wondered how many people on the Internet were going to complain about what an idiot Mirror Kirk is-it takes him forever to realize that Spock is in Auxiliary Control even though it's the most obvious place for him to have gone to try to take over the ship. But I think that was a very nice touch. Unlike Kirk-Prime, Mirror Kirk didn't earn command of the Enterprise. He used the Tantalus Field to leapfrog his way to the Captain's chair like a video game player using a cheat code, so of course he wouldn't be as good a strategist as his prime-universe counterpart. And once the Tantalus Field is taken away from him, he has no idea what to do. It's not at all surprising that Spock was two steps ahead of him the whole time.
This is a good point. And it really underlines that despite appearances there are a lot of disparaties between the two universes. It's not a perfect mirror, but a distorted one. The episode clearly illustrates that there isn't a great difference between Prime Spock and Mirror Spock while Mirror Kirk is nothing like Prime Kirk.
I agree that another five minutes or so could have been used in exposition to flesh things out a bit more.
We also see that Mirror Spock was adaptable. Prime Kirk had suggested that Spock find a reason to save the Halkans and make it stick, but that fell apart when he wasn't able to deter Mirror Kirk from his (not surprising) course of action and the Halkans were destroyed. And so Spock adapted his plan realizing that he had to take more decisive measures.
If there is one character misstep in this I thought it could be Chekov. The original Mirror Chekov seemed just as savage as many of the others while this time around he's more dialed back. Then again some time in the agony booth could have caused him to reconsider and mellow. Maybe his original assassination attempt was something he really wasn't suited for and he was in over his head. He did something youthfully impulsive and/or got roped into something by others more given to scheming. Note how one of the henchman switched sides and tried to curry favour with Kirk. And Prime Kirk seemed to recognize it right off and scotched it.
There is a sometimes simplistic approach to these things. In a realistic world even a dictator has to be able to trust someone to an extent. Even in a savage regime there has to be some measure of loyalty and even friendship even if born out of likemindedness and shared self ineterest. Some of the more succesful pirates of old could be ruthless with enemies and still be reasonably fair minded to their crew, and they would follow him more out of loyalty and shared interest rather than simple fear.
In truth one can really overanalyze these things. I still found this entertaining and decently executed overall.