As an aside, the entire Enterprise crew seems to have "a bug up its ass" about Spock spending any time in the captain's chair, as their behavior in both "The Paradise Syndrome" and "The Tholian Web" suggests. Some have attributed their behavior to poor writing, but it seems as though the crew becomes unruly whenever Kirk is absent. The only time that they seem to fall in line behind Spock is in The Undiscovered Country, as they willingly assist his investigation of Chancellor Gorkon's assassination.
Actually, isn't it mostly McCoy who has the issue? Sure, the crew would give glances when Spock was too literal or uncompromising (That Which Survives), but for the most part, Bones was the guy who crabbed about Spock being in charge. Uhura was just dandy with it, Sulu and Chekov never seemed to have a problem. Scotty bitched about "that Vulcan won't be satisfied until these panels are a puddle of lead" and he was also crabby about chasing a "wild goose" in Triskelion, but again, that had little to do with him being in command. They just didn't agree with his actions at the time. Not everyone agreed with Kirk at all times either (Scotty was always railing about going past warp 7 or something). In Galileo Seven, Scotty was his staunchest ally, but still questioned when he did something weird. That was Spock's fault, he never explains ahead of time.
I see it not so much as havnig a "bug up their asses" but more of a "he's an alien and so they don't quite get his motiviation for his decisions." Mostly, though, it's just Bones who's the crabby pain in the ass.