I haven't had this problem myself but what another post you mentioned means is following:
- Go to Visual Studio
- Search for a Work Item with ID from the error message you are getting (in your case 328)
- Open this Work Item (it should be a Test Plan) in Visual Studio and save it
According to the post Cannot view any Test Suites and Test Cases in TFS 2013 Web Access despite being able to access them in MTM this should solve your problem.
Update:
What do you see if you just open TFS Web access in browser?
Can you see this "Test" part?

Can you see your Test Plans in the list of test plans of selected *Team Project"?
If you can't see your Test Plans in the list change the Team Project (just click on this and select another one)
Further update:
Please check this article describing new permissions that was added with TFS 2013 Update3: Plan Manual Tests using Team Web Access
You still access test plans and suites using either the Team Web Access or Microsoft Test Manager. But make sure that you set up access based on permissions for the area path.
We didn't have this kind of issues after upgrade to TFS 2013 Update 3 so I can't help you much...
If you don't find nothing helpful in article above consider to contact Microsoft since it seems to be an Upgrade issue.