HttpContext is part of the System.Web namespace, which itself is within the System.Web.dll. Unfortunately the .NET Framework 4.0 Client Profile does not include the System.Web.dll and thus it doesn't know about HttpContext. There are some steps you can take, I'm going to write down two of them:
1) remove all references to System.Web (in which case you will have to remove log4net.Plugin.RemoteLoggingServerPlugin) to build it
2) add conditionals that exclude all references when built against the Client Profile
In case you do 2) please send us a patch together with the revision we can apply it to. The reason why we are able to build it is that we use a buildbot which builds it for us against a client profile with all modifications needed so that it works (I recall that Stefan did a lot of work there). Please someone correct me here if I'm wrong.