Troubleshooting Exchange roles and services

It's important to firstly make sure that all of the nesacsery Exchange servers are running:
Get-Service | Where {$_.DisplayName -Like "*Exchange*"} | ft DisplayName, Name, Status

And to verify that all the required Exchange server components are active:
Get-ServerComponentState -Identity <server-name>

We will have a look at the overall health of the Exchange Server:

Get-HealthReport -Identity <server-name> -RollupGroup

And then we can take a look at all of the monitors / probes in the "HubTransport" health set:

Get-ServerHealth <server-name> | ?{$_.HealthSetName -eq "HubTransport"}

or

Get-HealthReport -Identity <server-name> | where { $_.alertvalue -ne "Healthy" }

We then invoke the probe(s) that are causing the issue by specifying it below to make sure that it is not a transient error and to find out any details regarding the problem.

You should use the 'Identity' output of the following command to get the probe name for use with "Invoke-MonitoringProbe."
Get-MonitoringItemIdentity -Server <server-name> -Identity Store | more

Invoke-MonitoringProbe -Identity Store\ActiveDatabaseAvailabilityProbe\Mailboxes -Server <server-name>  | FL

Some of the errors I encountered on my lab setup were:
- Messages.failed.to.be.made.redundant.Monitor // Not to bothered about this one in my lab environment