Hi,
These are Joomla log files, not server logs. You can ask your hoster if the can tell you why you are getting these 500 errors.
As a workaround you can decrease the number of newsletters you are disolaying on your archive pages. You have set it to 20 and the last five ones are causing errors. Set it to 15 or less.
Reminder: After using Joomla debug, alwasy set your error reporting back to system default.