The concept of the command crew growing more and more obsessive with mundane tasks while one of the non-human crew stays calm and collective has been done prior on the Deep Space Nine episode "Dramatis Personae".
Mission Date: August 14, 2152
Trivia: This episode introduces the "Tactical Alert", and the "Red Alert" siren used in other Star Trek series. Temporarily jokingly called "Reed Alert" (after Lt Reed), this "Tactical Alert" is the predecessor to the "Red Alert" familiar from the other series.
Reed: (infuriated over Trip's focus on the captain's chair) This isn't a bloody pleasure cruise! Without proper discipline on this ship, this mission is doomed!
Trip: Why don't you go play soldiers somewhere else?
Reed: If this were a military situation, you'd be taken out and shot!
Archer: What'd you do? It seems totally different.
Trip: I lowered it... By one centimeter.
(angry over Trip ignoring his red alert in favor of fixing Archer's chair)
Reed: If this were a military situation, you'd be taken out and shot.
(both start fighting)
Archer: Hey, hey, hey, hey! (to Trip) I don't care what color the headrest is or whether it can serve me iced tea! I just want a place to sit when I'm on duty! (to Reed) And if I hear that alarm one more time, I may have you taken out and shot.
T'Pol: Are you feeling alright Commander?
Trip: ...I know you don't think this chair is important, but you're wrong. What's the most critical component on this ship? The main computer? The Warp Reactor? Huh...?! It's the crew. And the most important member of the crew is the captain. He makes life and death decisions every day, and the last thing he needs to be thinking in a critical situation is: 'Gee! I wish this chair wouldn't such pain in the ass!'
Reed: It's a chair.
Trip: It's the "Captain's" chair. It's just as important as your... Reed alert.
Reed: 'Reed alert'. That's not bad...