I think we have to keep in mind that language (for Wittgenstein) is based in use-value. Go back to Language Game #2, where you have builders calling out for building materials like rocks, beams, slabs, etc. Those words are only 'meaningful' as intermediaries or tokens expended within a system of interactive behavior. They have no intrinsic meaning, only extrinsic or intersubjective meaning.
This is why Wittgenstein says private languages are impossible. There is no 'other' in a purely private context, and thus no interactive behavior, so one cannot develop a use for words. Why would I use a word for (say) water if I am the only person who ever drinks or provides drink for myself?
Wittgenstien's problem with philosophy is not that it uses private language or fails to convey meaning. The problem of philosophy that W complains about is more at an incoherence in the language game being played. It's as though you sat down to play a game of chess and your opponent started playing checkers; as though builder A kept calling for the materials to build a well but builder B kept bringing the materials to build a house. The only way to fix that incoherence is to step back and find the place where we made the mistake in language — where one or everyone adopted the wrong set of rules to apply — and resolve that. After that, the philosophical problem goes away, and we're just left with playing out the game we finally agreed on.
If you say something wrong but still get your point across, it's because the other intuited (somehow) the language game you were trying to play, and accomodated to it. People have a knack for that, if they choose. But by the same token, you can say something perfectly sound and right and still fail to convey your meaning if the person you're communicating with does not care to adopt that language game and its rule-set.