The main benefit of types for me is not correctness but documentation and tooling. It's fine not to have types in code I write myself or with one or two others. But if I have to deal with a large codebase that I wasn't involved in writing then types make it so much quicker to understand. Just being able to quickly find all references to a type or all a method's call sites makes it possible to "reverse engineer" the design from the code.
This tool claims it can do advanced inference. If it were possible to hook it up to an editor or IDE to analyse existing untyped js in this way it could be invaluable.
We have some basic editor support, more is coming soon. Flow exposes several commands that are useful through an editor, like type-at-pos (give it a position, it gives you back the inferred type), suggest (give it a file, it dumps out an annotated file), autocomplete (gives you suggestions at a given position), etc. Also, we require annotations at module boundaries, so you're modules are going to have well-typed interfaces that serve well for both documentation and stability.
I strongly agree with module typing (and being more relaxed within). Because of caller dependence on modules, the difficulty of changing static types becomes a benefit. Plus, they need to be documented anyway; and tooling support helps use they as if they were primitives.
As others have said, I love the approach of inference giving static type benefits, for free. If you get tooling support, at no extra work, why not adopt it?
But static types can be a hard sell for JS programmers. What sort of reception has it gotten inside facebook?
Still early days but the reception has been strongly positive. We may be a biased bunch but we like our code mostly statically typed with the flexibility provided by dynamically typed languages. A large part of this culture is due to the immense internal success of Hack (http://hacklang.org/).
you should check out sublime text if you haven't already. ST3 reads your js as you type it, and allows you to navigate through the code like you would through visual studio, keeping a dictionary of where the words appear and guessing what they are as. Its not as good as a static languages navigational abilities (you may have to choose between jumping to Increment the function, and Increment the variable), but its still pretty good.
This tool claims it can do advanced inference. If it were possible to hook it up to an editor or IDE to analyse existing untyped js in this way it could be invaluable.