I've never liked Star Trek as an out and out comedy. This episode, like "I, Mudd," goes too far, dragging characters out of character to sell the jokes. While I don't think Tribbles was the best episode by a long shot, at least everyone stayed in character, making it that much funner. It's a different style of humor.
There is one laugh in this episode and it's from Spock: "I would advise ya's ta keep dailin', Oxmyx." But, again, it's way out of character. However, in his case, it's funny, because Nimoy underplays it. Shatner, on the other hand (and I'm his biggest defender), makes a meal out of the sets. Too much so.
This rates a 3 from me.