It seems to me that the most invaluable thing about a static/strongly-typed programming language is that it helps refactoring: if/when you change any API, then the compiler
I totally agree with your sentiment. The very flexibility that dynamically typed languages are supposed to be good at is actually what makes the code very hard to maintain. Really, is there such a thing as a program that continues to work if the data types are changed in a non trivial way without actually changing the code?
In the mean time, you could check the type of variable being passed, and somehow fail if its not the expected type. You'd still have to run your code to root out those cases, but at least something would tell you.
I think Google's internal tools actually do a compilation and probably type checking to their Javascript. I wish I had those tools.