Hi John,
The first problem you describe sounds like a script error in the browser rather than a server side error. In any case not knowing the specific error I cannot help with that one.
Of the errors you posted it sounds like the last one is the one you are experiencing when saving and it is the result of running a mojoPortal build that was compiled for .NET 3.5 under .NET 4.
You could solve that one by adding this to your Web.config file just before the closing </system.web> tag:
<httpRuntime requestValidationMode="2.0" maxUrlLength="560" maxQueryStringLength="2048" />
However, the best solution would be to install the latest version of mojoPortal that is compiled for .NET 4 (currently mojoportal-2-3-5-5-mssql-net40-deploymentfiles.zip). you would install it using the upgrade procedure since you already have a running version.
The other errors you posted would typically cause the design to not work (ie no css would render) and may be caused if the server is not configured correctly for the .ashx extension. But you have not reported that as a problem you are having so I'm confused. Also the structure of the url in those errors makes me think you are running an older version of mojoPortal.
Can you tell us the version of mojoPortal? You should see it at Administration > System Information
I would expect that Arvixe did install the 3.5 .NET build of mojoPortal since I think they would be installing it from the web app gallery, but I would expect it to not be an older version than the one we have in the gallery and the error makes me think it is older.
Hope it helps,
Joe