Sandboxed Solution with Full Trust Proxy

Problem: You deploy code as a sandbox solution however it fails as you need to go beyond the permissions a sandboxed solution can perform.  For example sandbox solution code cannot write to the ULS and security is restricted so you won't be able to use RunWithElevatedPrivileges.

Resolution: You can develop a full trust proxy that is deployed into the GAC, you also need to register the full trust with SharePoint.  Lastly, create the code for your sandboxed solution using the Full Trust Proxy code.  The full trust proxy performs the operations that are beyond what the sandbox solution code is allowed to perform.
Update 23 April 2011 - CKSDev is an extension tool for Visual Studio that has a SPI (template) to create a full trust proxy.  This will do all the plumbing of creating the full trust proxy and the deployment packaging.  So if you are wanting to add a Sandbox Solution Full Trust Proxy for Logging use the VS template provide and all you need to add is your logging code.

More Info:
http://blah.winsmarts.com/2009-12-SharePoint_2010_Sandboxed_Solutions__Full_Trust__Proxies.aspx
http://ranvijaysingh.blogspot.com/2010/06/full-trust-proxy-in-sharepoint-sandbox.html