Error pages
There is a variety of way different errors can happen in Moodle. Because they each happen under different circumstance there cannot be a single way of handling them, and where possible and desirable to customize them.
Types of errors
Normal Moodle errors
These types of errors are things like you tried to access a course which no longer exists, or access a course which you don't have access to. Because these are "Moodle" pages they are themed correctly and normally there isn't much you want to do to improve them.
If you want to change the wording of the errors see:
https://docs.moodle.org/en/Language_customisation
If you want to change the theme, that is one and the same as normal theme customization:
https://docs.moodle.org/dev/Themes_overview
Fatal Moodle errors
These types of errors are more fundamental, and something has gone wrong so Moodle itself can't load, which means the error page can't access the database, MUC, or the language and strings API.