According to Cracked, Gilligan's Island is based on the 7 Deadly sins... That means it actually makes sense:
Pride = Professor, Sloth = Gilligan, Lust = Ginger, Greed = Mr. Howell, Gluttony = Mrs. Howell, Wrath = Skipper, and Envy = Mary Anne.
The Season 2 episode Nyet Nyet—Not Yet! brings in some rare Fridge Brilliance to the series. The cosmonauts were more than willing to rescue the castaways, who would have remained prisoners of the Soviet Union (tropical island or Siberian gulag—where would you rather be stranded?) In any case, if the Soviets had rescued the castaways, they would have also had to admit that their space capsule landed far off course. Even if the cosmonauts (or the people they reported to) had the purest of motives, a rescue would not have happened for political reasons.
Why is the island called Gilligan's Island? In an early Season 1 episode, the castaways hold an election and elect Gilligan President of the island.
If the Professor can do so much with Bamboo Technology, why not just build or repair the the boat? Because they're on an uncharted desert island. Since they don't know where they are, they could get themselves killed by sailing off with no direction. A commonly taught rule is if you're lost, then you stay where you are until help arrives.
Doubles with Fridge Horror and Irony in the fact the storm may have blown them off course but it's not necessarily that of course so that it's very likely they're not that far from Hawaii. It would go a long way to explaining why they get so many visitors despite the fact they're supposedly an uncharted desert isle and why they're in range of a radio station. Hell, they might not even be uncharted (since it's not exactly a desert) and it's a Hawaiian bird sanctuary or national park.
The theme song originally ended with referring to the Professor and Mary Ann as "the rest" (until Bob Denver insisted they be referred to by name). This actually makes sense as the other three passengers are a movie star, a millionaire businessman, and his wife. The Professor and Mary Ann would probably be referred to as "the rest" because they're not as famous as Ginger and the Howells.
What would have happened if any of Ginger's attempts at seduction had worked? Or worse, if either Ginger or Mary-Anne had sex with anyone and got pregnant? Somehow, the idea of trying to raise a child on the island (let alone trying to give birth when they had essentially no medical tools and probably combined limited medical knowledge)...
Not that much of a problem. The professor could've made a maternity ward out of bamboo and sand.
And let's be honest, lots of women give birth every day outside of a modern medical facility without any fancy medical tools or training — the species would not have survived otherwise.
I think the real horror here is that a baby is being raised on an island that has been visited by gangsters, cannibals, Japenese soldiers, and far worse.
Why would all of them bring bags full of their personal belongings and all of their outfits for a third-rate three hour tour on a tugboat?
One possible answer: the three-hour tour doubled as a one-way ferry run between islands, and you brought your luggage because you'd need it at your destination. For a round-trip (which you wouldn't take your luggage on), you took the six-hour tour!
Another possibility: In some places in Hawaii, if your room is not ready when you arrive they will give you free tickets to a boat tour or other activity as a sort of compensation/ keep you busy till it is. While the chances of all of them being on the boat for that are improbable. It's a possibility.