Common activation issues for Microsoft 365 on a Mac include errors such as "No license found," inability to activate Outlook, repetitive sign-in prompts, reaching the installation limit, being asked to activate repeatedly after activation, and error codes like 0xD000000C, 0x8A010101, 0xD0001043, and 0xD000001c. These problems can stem from incorrect Microsoft Account usage, incorrect license selection, network connectivity issues, or permission limitations for system folders. Troubleshooting steps involve resetting credentials, fixing folder permissions, and using the Office license removal tool.