* Your type system cannot be sound. It's going to have escape hatches and exceptions because that's how dynamic languages roll.
* There will always be constructs that you can't type. See above.
* If your type system is going to usefully type enough of the ecosystem, it will be Turing complete.
All of these things are the trade-offs you make when you set out to layer types on a dynamic language, and they're well worth it to get 99% of the way to type safety in a language that otherwise couldn't scale. Theoretical purity is meaningless if the language isn't useful.