[Retra]

I don't think the problems are meaningless because words might have different meanings, but because problems are often posed as if the words can't have multiple meanings so questions are often arranged in a way such that any reasonable solution will end up contradicting the meaning of words in the question.

IMO, the best thing to take away from Wittgenstein is that he understood how words acquire meaning -- through usage in context -- and that two people can think they are talking about the same thing but if there is any difference in how they use the terms, or any variation in what contexts they consider them appropriate, then they cannot be talking about the same thing, because they aren't using the words the same way in the same context.

Learning language is like learning a certain kind of morality: which words are 'proper' to use in which order, situation, etc. (And you can always find stark disagreement where any moralities diverge.) The wisdom of all this is to instead focus on where people have agreement, by establishing shared definitions, axioms, or even participation in activities. These kinds of things are 'meaning multipliers'.