Using spatial dithering and the iphone 4's retina display, you could make an app that could display HDR and still have the resolution of the old iphone. Throw in temporal dithering if it was something like a static photo viewer, and you would have a pretty massive range.
That would just increase the resolution. The real problem is that the device is way too dark to display the levels of radiance you see on a bright day. Tone-mapping has to be used to bring those levels down, and there is no "correct" way to do that - one has to play with settings.
It wouldn't increase the resolution, it would increase the dynamic range; for two shots with different exposure you would do 4 pixels white if both were white, two pixels white if one was full white and the other full black, etc. (your flat panel probably already uses a similar approach to get roughly 8bits of overall color-depth out of 7bit elements)
I meant intensity resolution (or color depth, as you say). Dynamic range is something else - it is the interval [darkest, brightest], or their ratio if you prefer.
