In production you’ll want to monitor the usual suspects such as CPU, memory, free disk space, etc.
https://github.com/IQSS/dataverse/issues/2595 contains some information on enabling monitoring of Glassfish, which is disabled by default.
There is a database table called actionlogrecord that captures events that may be of interest. See https://github.com/IQSS/dataverse/issues/2729 for more discussion around this table.