There many important pages to keep an eye on for Office 365 including information in your tenancy around Planned Maintenance and Service Health but there are two that are worth keeping any eye that are hosted on the Office 365 community page.
Microsoft are always updating their products and one of the fastest they now do is Office 365 and to ensure you always get the best experience for your client machine support for new products begins as well as older ones expire. These include Windows XP ending on 1st Jan 2014 which is at the same time as Windows Vista. One the list it also recommends that Outlook 2010 is patched to a certain level.
This list is always being updated so ensure you keep an eye on it and make sure that your clients are up to date to allow your users the best experience with Office 365.
As part of being the Tenant Admin you will need to do system updates on your network to ensure your server and client based software is always up to date. This includes one that I didn’t know until I first read it here but your Exchange 2010 SP2 Hybrid servers will need to be on Rollup 4.
Add these two links to your navigation bar so your always keep an eye on them and know what is happening.