They seem to have taken fairly reasonable precautions. You can still reflect over the assemblies loaded in the AppDomain, so if you had time to poke through them, you might (or might not) find something in their custom assemblies that was interesting and exploitable, but it looks to me like the model is essentially what you'd get with a shared web host (plus the reasonable restriction of no file system or Internet access) and that model has been used to reasonably successfully isolate applications from each other and the host for many years now.
As I mentioned in my comment on Tyler's answer, they've also implemented some controls to prevent applications from mounting DoS attacks on the service, such as limiting application runtime to 5 seconds, and application memory to 200KB.