I had a really hilarious bug today where under some circumstances all the text in the display would be replaced by numbers. Small integers, each placed where the word should be.
What had happened is that I'd added a layer of indirection; where previously, after line wrapping, the data structure for a rendered paragraph was an array of pointers to the word objects, now it was an array of indices into the paragraph's word array. And I'd forgotten about one particular exotic code path. Lua was seeing the array of indices, automatically casting the ints to strings, and then using those strings instead of the word data itself...
Static types would have made this bug impossible.
...way back when, there was a really nice and thoroughly obscure language called Strongtalk; it was a Smalltalk 80 clone with optional strict types. You could annotate your classes and methods with type information. If it was there, it would be checked; if it wasn't, you got the traditional behaviour. The JIT knew about the type information and could use it to produce really fast code. It combined the ultimate dynamic language with an expressive static type system (complete with parametric polymorphism).
It was open sourced in 2006 and sank without trace. Sigh.