Tools for Troubleshooting Office 365

Check your Office 365 configuration with Office 365 health, readiness, and connectivity checks ;
Run checks to help determine the status of your on-premises or cloud configuration.
Details | Prerequisites

Check your on-premises Exchange Server with the Office 365 Best Practices Analyzer (beta)
Requires Exchange Server 2013.
Details | Prerequisites

Check your Office or Office 365 connectivity with the Microsoft Connectivity Analyzer
Requires Windows Vista or higher, with Microsoft .NET Framework 4.5.
Details | Prerequisites

Check your network connectivity with Exchange Client Performance Analyzer (ECPA)
Run checks to help determine the health of your network.
Details | Prerequisites