I did take a quick look at your portal screens, both the custom "Customer_Portal" and stock Contacts_Portal. Unfortunately, I can't seem to recreate this error myself, I have logged in to the Contacts_Portal from my PC, MAC, and an iPhone and all loaded just fine with no errors. Any chance you can give us a screenshot of the error you are referring to?
2) In regards to your question about New Appointments not showing up in your Method Calendar. When I first went in, I didn't see any recent Activities or Appointments for any users in the Activities List. However, when I went to export your Activity list, there were actually hundreds already created, included 3 test Activities I created. Because these Activities show up on the Table export, but not the grid, this somewhat makes sense why they aren't showing up in your Calendar. The issue here is that I see some customization done on a few of the screens (some could be interacting with your Calendar), and as a Support Rep. we can't troubleshoot custom screens.
Here is a link to get more information on our Consulting Services, how to contact them, and some pricing. Consulting should be able to help you work these issues out, and likely can help you over the winter with any other Customization you would like to be done.