You may have seen click heatmaps before -- they're a visual representation of where user mice have clicked on a web page. The iPad, as this post from Design Language News shows, has its own built-in heatmap: the oils and residue left on the iPad's screen after you use a certain app. It's kind of gross, sure (usually, people are more concerned about wiping this stuff off than learning anything from it), but as you can see from the pictures, the fingerprints can provide some interesting insight into apps and how they're used.
You can see, for example, why the iOS UI puts rarely-used or navigation buttons on the top of the screen. Since most of our usage is right around the middle, developers want to make sure that buttons that require any traveling also have a suitable importance of function and thus are prominently displayed. And you can see the simplicity of certain apps, too, as Angry Birds and the YouTube app only have a few controls, while a game like Fieldrunners can get relatively complex.
Interesting stuff, all divined from smudges we wipe off daily. I don't think Apple provides heatmaps like these to developers, but maybe some coders trying to figure out how their UI is used can check the fingerprints after a usage session and see what they learn.