After upgrading to iOS 6 we started having the issue in our application.
We have long forms where user enters data. When the field that user focuses is pretty close to the end of the page, when the keyboard is shown the footer jumps up and, when we start typing something it either disappears totally or jumps to the middle of the screen.
When we hit done the footer is repositioned back to the bottom of the screen.
NOTE: it is important that this happens only at the moment we start typing, not when the keyboard is shown.
Also, it happens in both UIWebView and in Mobile Safari with both jQuery Mobile 1.1.0 (that we use) and 1.1.1.