Type inference (and as a consequence parsing?) in ML 'and I suspect many other functional languages, is complete in deterministic expotential time. For any practical reasons that's as close to undecidability as possible.
Comment on Re: Perl Cannot Be Parsed: A Formal Proof
No, you can parse SML without doing type inference. The (only) tricky part of SML parsing is operator fixity, which doesn't depend on types at all.
And yes, SML type inference is superexponential, but only for contrived examples. So for "any practical reasons", it's not even remotely close to undecidability.