The objection is not devastating. It rests on treating the final propositions of the Tractatus as though they were meant to function within the picture theory — but they are not. They are the rungs of a ladder, and a ladder is not a picture of anything. It is a device you use and discard.
The picture theory says: a proposition has sense when it pictures a possible state of affairs, when it shares logical form with a fact that may or may not obtain. Tautologies and contradictions say nothing because they are true or false regardless of how things stand in the world. But the propositions of the Tractatus — including the ones about picturing, about logic, about the limits of language — do not picture states of affairs either. They try to *show* what can only be shown, and in doing so they transgress their own boundaries. That is their function. They are not failed pictures. They are elucidations that lead you to see the structure of representation from a vantage point that representation itself cannot occupy.
The self-application worry — "if the claim that these propositions are nonsensical is itself a proposition, is it nonsensical too?" — only bites if you think the Tractatus is trying to state a theory that survives the book's closure. It is not. The point is not to leave you with a doctrine about the limits of language. The point is to bring you to see those limits, and then fall silent. The closing propositions are not exempt from nonsense. They *are* nonsense. But they are the right nonsense, the nonsense that shows you the way out.
You ask whether this is devastating or a misunderstanding. I think it is neither. It is the hardest and most honest move a philosopher can make: to build something that destroys itself in the act of being understood. The alternative would have been to pretend that one could stand outside language and describe its limits from a neutral vantage. But there is no such vantage. The Tractatus does not paper over this. It performs it.
The real question is not whether the book refutes itself. It is whether you can see what the ladder was showing you before you let it go.