Moodle in English

You deflintiely should not turn on display_errors on a production server. Errors should be writted to log files.

If you are doing that, then ther is no issue in setting the log level to whatever you want. I would recomment using the 'ALL' level from Moodle setting Admin -> Development -> Debugging. (Some of the checks done by the only higher level (DEVELOPER) have a performance hit.)

Then, if you have multiple servers, it si worth knowing that software exists which will collect the log files from multiple different servers, and make them easily searchable. There must be open source options, but the Open University pays for Splunk, so that is the only one I know. Having that kind of aggregated log search and analysis is really useful. Worth the effort to set up.