Pg. 54
You are correct that there would normally be a の nominalizer in that situation. I have had to look this up before, but seems I didn’t save the link, but the gist of it is that classic Japanese didn’t have that nominalizer, and so nowadays, the plain form verb + がいい is used almost exclusively in media to convey pompousness, and an almost imperative sound to it.
It’s pretty old-fashioned sounding, and you won’t see it much outside of media that is either set in classic times, or with characters who are being dramatic, like Nishikata here, who dabbles on the chuunibyou side a bit here and there. 
As opposed to:
先生におこられのがいい meaning, “The teacher scolding (Takagi) would be/is good.”/“The teacher getting mad (at Takagi) would be/is good.”
(Editing to clarify, I used direct translation above to maintain the structure, but がいい is more akin to “I would like” or “I want” in natural English than “is good”.)
Without the の, it conveys a sense of, “The teacher had better scold (Takagi.)”/“The teacher had better get mad (at Takagi.)”
At least, that’s my understanding. I’ll dig around for that link, and if somebody corrects me in the meantime, they are probably right.
verbs - The meaning of ～がいい - Japanese Language Stack Exchange
This is what I’m finding for now to support my statement (seems the modern form of it would be verb +方がいい, if you wanted to drop the level of pompousness and not sound like you are using classical Japanese). It’s not the best link, and not what I read before, but figured I’d drop it while I continue my search).
Pg. 55
Actually, I’m glad you asked about this, because this threw me a little and I meant to, but forgot!
I think that the なんだってさ is actually a shortened:
なのだ + ってさ
Wherein なのだ is item 1 on Jisho here: Jisho.org: Japanese Dictionary
And ってさ is indicating hearsay (well, って is. The さ is just the ending particle implicating slight assertion, I think.)
The part that confused me was なのだ sounds so certain, and combining it with the hearsay. My interpretation came out to be along the lines of:
“We are definitely moving seats today, I hear.”
But it just felt weird having a definite sentence attached to an, “I hear.”
I definitely would like to hear other’s thoughts on this. I might be off base on what the なんだ is contracted to, but that was what I eventually felt fairly satisfied with.
I mean, with those style of desks, I think they have cubbies to store their books and notebooks and the like, as opposed to carrying everything in a backpack. It might just be a case of it being more convenient to move the whole desk as opposed to trying to carry all of that stuff in their arms at once? Since all the desks are occupied, it’s not as though they could just move stuff over to the new desk easily without being in the way of whomever they are swapping seats with.
I’m just speculating though. It does seem a little messy, I agree.
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I also really liked the next panel with Mano, “Oh, don’t mind me… I’m just depressed…” gave me a bit of a chuckle at her expense.
