Office Web Apps can be used only by SharePoint 2013 web applications that use claims-based authentication.

Office Web Apps rendering and editing will not work on SharePoint 2013 web applications that use classic mode authentication. Hence, something to watch our when migrating SharePoint 2010 web applications.

Versioning

Do not enable minor versioning in document libraries that contain OneNote notebooks. Minor versioning can result in synchronization errors that prevent edits from being saved.

Technical References:

Default crawled file name extensions and parsed file types in SharePoint Server 2013

User permissions and permission levels in SharePoint 2013

Create and deploy a thesaurus in SharePoint Server 2013

Software boundaries and limits

This will be a work in progress posting, as I'll add when I encountered them.

When I was branding an Office365 SharePoint 2013 site, I'm getting an error when viewing apps that use Web Parts.
The error message is "This content cannot be displayed in a frame" and is described similarly to this forum thread.

http://social.msdn.microsoft.com/Forums/en-US/appsforsharepoint/thread/fa6abb31-7251-4744-ab14-634cde38a42d

The "temporary fix", is to add “https://login.microsoftonline.com” to the Trusted Sites list in Internet Explorer.