Goofs?

well, not goofs really, but then..

Peter Sellers has a surname 'Bakshi' which isn't quite a South Indian surname though he speaks in a South Indian (specifically, Tamil) accent.

also...though he is amazing throughout, he still loses his accent albeit very slightly at some places

and the comment he makes about the elephant being the 'symbol of our country' - not really true (though the world associates the country with wild elephants and snake charmers!)

also - if you notice carefully - his facial makeup varies between scenes. Sometimes he is quite dark while at other times he looks absolutely fair

...but then, who cares. Forget about it and watch it again, and again, and again...he is simply outstanding.

I had read that Blake Edwards did not have much of a screenplay and Peter Sellers and most of the actors simply hammed their way through for most parts of the movie. Now, that takes some doing.