Well, it's OK for his 1st officer friend to give him a bit of a back rub, but when it's the Yeoman? Well... there's a little sexual tension there, especially with that "throbbing" motion. I think that's why Kirk reacts that way and feels embarrassed.
I, Mudd - this may be the funniest of all the episodes. The whole thing is campy from start to finish, with the clueless androids. Best scene was the play acting by the crew to fool them.
A Piece of the Action definitely has some very comical bits to it. Half the episode seems to be tongue-in-cheek, with everyone playing "gangsta", including Spock.

Trouble with Tribbles is cute... but it's more or less a little bit of chuckling here and there.
Shore Leave has some pretty funny moments, like Finnegan's altercation with Kirk. And witty remarks by Spock. Plus McCoy's return at the end.
Squire of Gothos is a bit funny with the outlandish and brash Trelane.
Plato's Stepchildren has a good bit of humor in it. Especially that scene with Kirk mimicking a horse, and Spock doing the flamenco dancing around the supine Kirk. Of course, you have to look past the terror aspect... these people are being manipulated. But face value it's pretty hilarious.