While I think Aaron Brager's answer is the ideal appraoch, my app needs about 15 different appearance settings and uses a split view controller, so I have to reapply all the setting to the global appearance and then apply them all to my two displayed views. That's a lot of redundant code.
Based on the idea that presenting and dismissing a modal view controller forces everything below it to redraw, I tried this and it worked perfectly:
UIViewController *redrawTrigger = [[UIViewController alloc] init];
redrawTrigger.modalPresentationStyle = UIModalPresentationFullScreen;
[mySplitViewController presentModalViewController:redrawTrigger animated:FALSE];
[mySplitViewController dismissModalViewControllerAnimated:FALSE];
[redrawTrigger release];