Mailbox Server Role: 

1.Mailbox\Public Folder Database Status – Get-MailboxDatabase –Server “Name of the Server” –Status | ft Name, Mounted
2.Service Health – Test-ServiceHealth –Server “Name of the Server”
3.Storage group copy status – Get-StorageGroupCopyStatus –Server “Name of the Server”
4.Backup Status – Get-MailboxDatabase –Server “Name of the Server” –Status | ft Name, lastfullbackup, lastincrementalbackup
5.MAPI Connectivity – Test-MapiConnectivity
6.Replication status – Test-ReplicationStatus
7.Cluster Mailbox Status – Get-ClusterMailboxServer 

Client Access Server:
1.Service Health – Test-ServiceHealth –Server “Name of the Server”
2.OWA Connectivity – Test-OWACConnectivity
3.Active Sync Connectivity – Test-ActiveSyncConnectivity
4.POP3\IMAP4 Connectivity –Test-POP\IMAPConnectivity

Hub Transport Server:
1.Service Health – Test-ServiceHealth –Server “Name of the Server”
2.Queue Status – Get-Queue –Server “Name of the Server”
3.Mail Flow –Test-Mailflow

Unified Messaging Server:
1.Service Health – Test-ServiceHealth –Server “Name of the Server”
2.UM Connectivity Test – Test-UMConnectivity -ListenPort 5060/2061
3.Active Call Status – Get-UMActiveCalls

Edge Transport Server:
1.Service Health – Test-ServiceHealth –Server “Name of the Server”
2.Queue Status – Get-Queue –Server “Name of the Server”
3.Mail Flow – Test-Mailflow
4.Edge Synchronization –Test-EdgeSynchronization

Additional Note: Event Log info on corresponding server can be found out by: –Get-EventLog Application\System |Where { $_.Type –eq “erro” }