I 'fixed' (not sure if it is a permanent fix yet) by looking at the source for the web page and then adding any of the additional sites that were referenced. You'll see that c.mmcdn.net is the main reference. However, just adding this in as bookmark to parental controls doesn't fix the problem.
If you do a nslookup (from a terminal) on c,mmcdn.net, it returns two more aliases - c.mindcandy.cotcdb.net and 10005.mindcandy.cotcdn.net
Once I'd put these additional entries in, the page loaded ok.
The reason I'm not sure if this is a permanent fix is that the Moshi Monster servers may change their main sites, but the approach should be valid.