You can easily do that in a statically typed language as well; you just have to do it explicitly. For instance, Haskell has the error function, of type "String -> a"; you can use it absolutely anywhere, no matter the expected type, give it an error message, and if the value it produces is ever actually used, it throws an exception with the specified message.
Don't discount the value of doing it implicitly. When you're just throwing stuff together (and there is a place for that), it's a distraction to work around parts of the system that won't work yet, both the typing and the mental overhead.
Having done this both with Clojure and Erlang, I find the unversioned, dynamic mode of achieving this is fraught with trouble. It's really easy to end up in complex atypical states during upgrade which can at best be hard to debug and worst corrupt other, longer term state.
Exactly. I think what a lot of people miss is that erlang makes live upgrades possible but certainly not easy. Trying to upgrade a complex application one component at a time (the way erlang/otp promotes) is still insanely hard and not worth the pain unless you're working in a domain where you have absolutely no choice (which is of course why Ericsson developed erlang in the first place). For the vast majority of applications the right choice is to restart the server and accept a few seconds downtime.
I think with better documentation I'd actually call Erlang's model "easy" in that its really easy to do things correctly with absolutely minimum chance of corruption/failure/non-repeatability. OTP gives you the tooling—releases, versions thereof, and simultaneous multiple module tenancy being key—to actually do a good job. That's a rare thing.