A few weeks ago I started to notice a 30 to 70 second delay when making changes in either the EMC or EMS. The changes ranged from Enable-Mailbox to Set-MailboxFolderPermission. I noticed while running the New-Mailbox command with the -Verbose flag the delay was between "Admin Audit Log: Entered Handler:OnComplete." and "Admin Audit Log: Exited Handler:OnComplete.". In the example below you can see there is a 73 second delay.
Although familiar with the Admin Audit Log, the following was figured out by Microsoft over the course of 2 days :). After capturing some .etl traces it was determined that he arbitration mailbox used by/for the Admin Audit Logs was inaccessible. Turns out that another tenant in our enterprise (the first tenant but not the primary) held the arbitration mailbox used by the Admin Audit Log on one of their databases, a database that was taken offline a few weeks prior. As soon as that database was brought back online and I moved the arbitration mailbox to one of our online databases the delay mentioned above went away.
The lesson to be learned here is always know where your arbitration mailboxes are!