Google Apps Toolbox is a collection of tools which could be used to debug 'Google Apps'.
Most of the tools provided on this website do not require users to authenticate, but a few which require user data access may prompt for oauth credentials.
Browserinfo is a browser based debugging tool to capture client side info and look for obvious issues which may impact their experience on the internet.
Messageheader allows users to analyze SMTP message headers which often have sufficient information to help identify root cause of slowness. In addition to detecting misconfigured servers it can also explain mail routing which is often related to the source of delivery delay.
Other Tools which could help you debug Google Apps.