Formalize errors, esp. client vs. server

We should formalize the errors we throw (e.g. in cases where we have custom messages, like connection errors, or "node doesn't exist", etc.), but most importantly, there should be a documented way to determine whether a thrown error is due to a client mistake (e.g. "node doesn't exist") vs. a server one (e.g. connection error). This generally maps pretty nicely to HTTP 4xx vs. 5xx status codes.
