In working on some content related to SharePoint Online, I ran across this very useful reference for what does and does not work with SharePoint 2010 (and therefore SharePoint Online) using different browsers. The browser you use makes a difference in terms of the SharePoint Online features that work. For example, mutliple file uploads is generally not available in any browser other than IE, and even then, not when using the 64 bit version.
This can make a significant different when planning to deploy Office 365 and the SharePoint Online service description does not cover the details of specifically which features are and are not functional in different browsers.
So I was happy to find this reference http://technet.microsoft.com/en-us/library/cc263526.aspx called "Plan browser support (SharePoint Server 2010).
In short, according to this article the only browsers with no known limitations are 32 bit and IE 8 and IE 9, but the SharePoint Online Service Description does not list IE9 as supported browser.
Additionally, the document is a bit dated as the last version listed for Firefox is 3.6 and the latest (as of this writing) is 7.0.1.
So the SharePoint Service description is vauge about what does and doesn't work with different browsers, and technet article seems dated.
Microsoft needs to do better than this. We need a better reference for browser support for SharePoint Online.