Distinguish between internal errors and user errors

Currently all errors use `invalid_argument` and don't specify whether it is an internal error (i.e., bug) or user error. For an HIT user, it would be valuable to know the difference so that they know whether to report a bug or fix their code.

The issue names no file, test, or entry point. Start by locating the C++ uses of invalid_argument and reviewing how errors are currently surfaced; done means internal errors can be distinguished from user errors so HIT users know whether to report a bug or fix their code.

Written by the indexing model from the issue text.