The Exchange Product team posted a new useful tool that I started playing around with called the Mail Flow Guided Walkthrough (GWT) - http://blogs.technet.com/b/exchange/archive/2013/09/03/office-365-mail-flow-troubleshooter-now-available.aspx.
You can access the tool here - http://support.microsoft.com/common/survey.aspx?scid=sw;en;3568&showpage=1.
What it will do is ask you basic questions that challenges you may have and help you debug them. There are several scenarios for Office 365, Exchange Online and hybrid. I see this as a very useful tool to help with debugging initial deployments as well.
For instance I followed the path for checking to see if an Exchange Online mailbox is having issues sending an email. First you need to check if DNS is configured. Second check your NDRs. Third check the health of the service. Fourth run a message trace report. Fifth check the users Outbox, connectivity, third party add-ins, OST files, etc. Really found this to be a great tool.