The compiler does not catch your logic bugs. But stronger, more expressive type systems catch syntax bugs and structural errors like you wouldn't believe. It's not an all or nothing.

I have spent an embarrassing amount of time troubleshooting a < that should have been a > (in F#) where it actually resulted in a very subtle defect. I'm not aware of a type system that works have prevented this and yet,I do strongly agree with the assertion that in more strongly/statically typed language, "compiling successfully = very likely to run correctly."