"Extremely quickly" -- if you can always take all sides of every branch in control flow. And you'll find only the same errors -- if you restrict the types you define to those supported by the dynamic language. If you don't restrict yourself, however, you can start catching classes of error at compile-time that in a dynamic language you could only look for by writing your own runtime checks.

And runtime checks aren't free - they cost CPU, they can have their own bugs, and they can be tedious to write. "In general", rather than even try to be as careful in a dynamic language as you could be with an advanced type system, you'll just settle for not being careful.