Traditional applications runs on a single server and auditing concerns a single machine. (i.e. one OS the monitor etc.)
Logging infrastructure often produce a log file which is written to that same machine.
In the cloud things are different.
Application running runs on a grid of machines. Every Windows Azure role has many instances.
Each machine can continue to log its state like in the traditional case but to see the whole picture all the information from all the machines must be collected. This can be quite tedious.
This is were Windows Azure Diagnostics come into play.
Windows Azure Diagnostics aggregates information from all the running roles into one central location - Azure Storage.
It is possible to argue that Windows Azure Diagnostics is actually an aggregation system more than it is a diagnostics infrastructure.
With Windows Azure Diagnostics in place developers can continue the use the same logging skills and tools. No new development and effort is required. Applications will continue to log like in the traditional single server scenario. The only difference is that Windows Azure Diagnostics will aggregate the information to Azure Storage. The analysis should be done on the information collected from all roles.

Manu
Claim based identity is the future of identity management. It is simple, powerful and extensible but the most important reason to use it is the fact that it delegates identity management out of the application.
WIF is Microsoft's infrastructure for using Claim Based Identity. (Similar to what is WCF for networking)
Recently an excellent Training Kit was released about WIF and the integration of WIF with AppFabric Azure ACS.
I strongly recommend to download read and learn.
Manu