Google Apps Toolbox is a collection of tools which could be used to debug 'Google Apps'.
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.
Log Analyzer provides a way to analyze log files generated by Google products. For example, ChromeOS Logs, Google Apps sync for Microsoft Outlook, Google Apps Directory Sync, etc.
Loganalyzer for Google Drive is a log analyzer for Google Drive for Mac/PC, able to handle large log files, with lot of filtering abilities.
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.