Lansweeper starts off by collecting the CRITICAL alerts... you can use the following built-in report to get started
Windows: Error events generated in last 7 days
and filter by the eventID's, or sources, you wish.
WARNING: you can tell Lansweeper to collect other levels of events in addition to CRITICAL - but I really don't recommend that as it will grow your event log table by a TON. and then LS will slow down and you'll have to run database maintenance and shrink the table.
fortunately, sql replication errors, domain trusts, group policy errors, unexpected reboots, and more are all contained in CRITICAL alerts.