Do other branches have health and comfort inspections in their barracks or is it just the Marine Corps?

We used to have "Health and Welfare" checks periodically when I was a young Airman in the barracks. Usually only had them about once/twice a year unless problems had been recently noted. Later, as an NCO myself, I had occasion to accompany the 1st Sgt during a few inspections.

You could really learn a few things about your troops during those times.... lol

It's not "just" for the items you mentioned. Back in the days of Quonset huts and squad bays you'd be shocked at how often you could walk into the squad bay and it smelled like rank cheese. Some service members go straight from Mom's house to the recruit depot, to MOS school, and then hit the fleet. They literally don't know how to use a washer dryer. They don't dispose of uneaten food. And Mom scrubbed their toilet and shower. Until they acquire the necessary habits, what gets inspected gets done.

Unless something (usually an odor or something to mask an odor) started coming from the room, the CoGy and 1stSgt let the NCO's alone, except for quarterly "junk on the bunk" inspections.

We all have them. The Army calls them "health and welfare" inspections, but it's the same thing.