Get and output of all mailboxes, sorted by size, with items:
Get-MailboxDatabase "Mailbox Database 1" | Get-MailboxStatistics | Sort totalitemsize -desc | ft displayname, totalitemsize, itemcount
Paul Cunningham’s health check script for 2010/2013:
Generate Health Report for an Exchange Server 2010/2013 Environment
Public Folders:
Get a list of all mail enabled folders:
Get-MailPublicFolder | fl Name,EmailAddresses
Get-PublicFolder "\" -Recurse -ResultSize Unlimited | Get-MailPublicFolder -ErrorAction SilentlyContinue