Generally improve validation and exception messages

[jlstevens]

This is a general issue about improving the user experience when things go wrong. Sometimes our exceptions occur deep in the code when the condition that causes the problem could be validated much earlier with a better exception message and traceback.

We have had specific issues about this (e.g #1127) and some PR have improved the exceptions in specific parts of the code. This issue is for us to have a general overview of how things are progressing - new PRs improving exceptions can reference this issue.

Lastly, we might want to consider defining more of our own custom exception classes.