The Database Diagram Tool in SQL Server 2008 (Katmai) Management Studio has (once again) not changed much from the previous version.
Scripted Diagram export still works
This script to 'export' diagrams to SQL file (designed for SQL Server 2005) works in 2008. Implies there hasn't been any change to the storage format, and probably diagrams scripted in 2005 can be 'rehydrated' in 2008.
Diagram context menu unchanged
Nothing new in this menu - although I had forgotten the Copy to Clipboard item existed...
Table context menu adds Spatial Indexes... item
New spatial types can have their indexes setup just like other index types
Scroll down to Spatial Indexes on this post and these explanations of spatial indexes for a brief explanation of 'how they work'
(and no, this dialog doesn't actually resize in Management Studio - it's been Photoshopped for clarity)