To answer the question at the top of the thread: no, "we" haven't Gone Completely Bloody Mad. What's happened is merely that, as usual, a non-story has been seized on by a tabloid, splashed as a huge headline, while almost certainly (as Gromit said above) leaving salient facts out. All this has then been taken as the basis for asking if the country's "gone mad", and as being "PC gone mad", with a token whinge about health & safety (gone mad, perhaps?) thrown in while we're at it, etc etc. In other words, exactly the reaction the tabloid wanted by splashing the non-story in the 1st place.
As for the stuff about the use of "going for a chinky", "going down the *** shop" etc, mostly those references aren't racism as such, but just stupid lazy unthinkingness. Some would argue that the casual use of those words helps to create an environment in which taking the next steps to actual harmful offensive racism is made easier. Discuss!
It's on the same level as Jade Goody's "Shilpa Poppadom" comments. Not racist, but stupid and dimwitted.