My theory about the show...

I don't have any evidence of this like comments from the writers, but I'm pretty sure the writers quickly got tired of all the comments about how illogical the show was "why did they carry luggage?" "how did they fit all the stuff in the boat" (they even had to make a storage hut) that the writers thought "if people get this worked up over illogical things in a silly comedy, let's really give them stuff to get worked up over."

So, I'm pretty sure the writers decided to put in at least one completely illogical thing in each episode.

My three favorites are
1.When Gilligan finds a map, and the professor realizes it's a map showing the location of the island and all the neighboring islands between their island and Hawaii, but then tells them it's useless because it's a map for how to get on to the island, not how to get off of it.

2.When Gilligan carves the bathtub out of a tree and the Skipper commends him because the bathtub doesn't even leak, but nobody realizes they can easily carve out trees to make canoes to get off the island. (They could have connected the canoes together like in the opening of Hawaii 5-0.) Even if the canoes wouldn't have been sturdy enough to get back to Hawaii, they could easily have gotten them to an island in the shipping lanes. The professor mentioned several times that all the needed to do was get to an island in the shipping lanes to be rescued.

3.When they blow up the volcano by throwing a bomb into it. Leaving aside the bad physics, thanks to Gilligan, the volcano has already erupted before they could throw the bomb in. However, after they throw the bomb in, all the lava already out of the volcano sucks itself back in. It's a very funny sight-gag though, which I'm sure was the main purpose, but it's still absurd.

To be sure, some of the examples I would use as evidence of 'illogic' are maybe questionable. Like in the episode with Harold Hecuba where they write a musical about Hamlet in a single day. In this case it's not like all t.v shows and movies don't do similar illogical things like that in order to make the t.v show or movie work, but I think this is a 'bit' extreme.

For instance, in Star Wars: the Force Awakens, the First Order apparently trained something like 1 million soldiers without the new Republic having any awareness. And, if that's not illogical enough: who trained all these soldiers? Who fed all these soldiers? Where did the financing come from to do this things? Of course, this is why people say 'it's just a movie' or 'it's just a t.v show' but write an entire musical in one day? That's still a bit much.

I think that episode is brilliant though. The two songs from their musical are so good the episode should have been nominated for an Emmy.

On another matter, tv shows weren't really in any order back then and all that meant (no character growth, nothing episodic) but there was one thing that carried over from one episode to another, though I'm sure it was more for practical filming reasons than anything planned.

In the episode where the Japanese World War II fighter comes to the island, Gilligan ends up taking his gun (and his glasses too.) In a later episode where they need a gun for some reason I can't remember, Gilligan brings them the gun he got from the Japanese fighter.