You've Been Disconnected - S2-E17
Plot hole: Gilligan foils the rescue attempt by saying that before the storm, he wrapped up the telephone wires real good with the professor's rubber glue so they won't get wet... But the scene before this, all castaways were testing the phone when a storm instantly hit them without warning. Gilligan wouldn't have wrapped up the wires since there was no storm til the last second (in which they all ran and abandoned the wires).
You've Been Disconnected - S2-E17
Character mistake: Upon learning after the storm that the telephone cable was washed back out to sea, the Professor mentions the cable will eventually corrode and break and the Skipper says then a repair crew will have to come out and fix the cable so they'll be rescued. How? The cable is out to sea and a repair crew would never even get to the island since the cable's not there.
Answer: Bob Denver answered this when he was on a talk show hosted by Pat Sajak. He said they were going to write into an episode where the castaways found all these clothes, but it got too complicated, so he said, they decided, "who cares, it's only a TV show," and forgot about it. So the writers and actors even asked this, they just never bothered to address it.