The most important thing, if you haven't already, is to set the noImplicitAny and strictNullChecks compiler flags. I find that not having these flags set is a common source of Typescript type unreliability.

The flags prevent two behaviors that are a major source of type failures: defaulting some types to "any", and allowing null/undefined to be valid values for ANY type (!). Enabling these flags for an existing codebase is likely to uncover hundreds of type errors that are papered over with the default compiler settings.

W.r.t. upstream types for libraries being wrong, I find the silver lining here is that libraries will usually be happy to accept patches for their types, often with significantly less fuss than a patch to the actual code.

edit: Even with those in place, I also notice that Typescript types are not 100% trustworthy. This often comes down to unsanitized input, use of the "as" keyword, or hidden type violations. The conclusion I've come to is that it's just very hard to type Javascript code, partly because the values themselves are so prone to being mutated. So I agree that Typescript doesn't feel like the perfect solution to me. (I usually use Clojurescript these days).