Dell to Stop Using Indian Call Center for Corporate Customers due to customers complaining "that the Indian technical-support representatives are difficult to communicate with because of thick accents and scripted responses."
So that language barrier is still there - the difference between someone who's learnt English over a couple of years, even, and someone who's spoken it all their life, nuances included. I suspect it's more of a "language culture" barrier, i.e. the particular nuances of a language, rather than any syntactic or grammatical differences.
So, despite call centre jobs generally being tedious and scripted anyway, having someone on the other end that you know knows what you're talking about when you insult them does really matter.
I'm not sure just how specific this is - technical support is quite a personal thing, really, in comparison to, say, banking and accounting, or other call jobs that are more or less automatic, and require less "individual troubleshooting". Certainly manufacturing jobs are safe overseas.
The other question is, in the long term, how long til the offshorers do pick up on all the nuances and/or culture? How about if you taken into account increased media proliferation to such countries, and the increased instillation of American pop culture?