How do I clean up old warning and Error messages?

Assuming you are referring to DataSource checks (your typical CPU, memory, storage, network, etc) and website checks, you "clean" them by resolving the cause of the alert. LogicMonitor will automatically clear/clean alerts once the cause of the alert is fixed or you "tune" the alert settings so they are no longer in an alert state. You can acknowledge an alert letting people know you are aware of the issue and looking into.

For example if you are at 90% free on your server's C drive, LogicMonitor will keep that alert active until you free up space on the C drive, or you tell LogicMonitor (via Alert Tuning) to only alert when the drive is at 95% instead.