I've heard that Apple didn't change the touch input part of the new iPad's display when they upgraded to the Retina screen.
Is the touch response accuracy pixel-per-pixel perfect on the iPad third gen or is it lower?
Having just googled, I can't find a definitive answer to your question.
However, intuitively, I'd say that I can't see any way that, with a finger, you could select a point with accuracy anywhere close to 264 pixels per inch (see the Display section of the iPad technical specs).
And none of the Stylus reviews I've seen (such as this recent one from The Verge) suggest that any available styluses/stylii can reach a significantly greater accuracy than a finger - presumably because of the capacitive nature of the display: see e.g. this from Wikipedia
Internally, meaning Apple apps using APIs not available to third-party developers, I can't say for sure.
Public APIs (every non-Apple app on the app store) still receive touch coordinates for new iPad as floating point numbers in a coordinate system bounded by 1024 height and 768 width. This is the same as happened with the iPhone 4: while actual resolution doubled developers continue to process coordinates from and address the display as if it has 320x480 resolution, not its actual 640x960.
Developers can know that the display is double resolution by looking at the view's scale property but simply doubling the coordinates doesn't increase resolution, just the size of the values.
Like Clare says, the tip of your finger or a stylus just isn't any more accurate than that. So probably even Apple apps which might be able to access retina-resolution coordinates wouldn't bother. Reporting actual coordinates of touches at 264ppi is roughly equivalent to reporting points made by a precise application of a 0.1mm technical pen!