So right now the biggest issue with the latest iPhone firmware release is the splitting of iTunes accounts. You can read more about this issue on the net but basically people are getting the Black Screen of Death when installing iPhone Apps or they are not able to run their App Store apps anymore due to the account splitting.
I had the issue with my Apps not running anymore a few days ago. To fix it, I connected my iPhone to iTunes through my computer, uninstalled all the Apps through iTunes, then reinstalled them all through iTunes. It took a while but it worked.
I've had my iPhone crash during App installs and have gotten the Black Screen of Death three times now. Here are a few hints for avoiding the BSoD until a firmware update fixes this:
(1) Do not install more than one App update at a time
(2) When installing an App, do not use the iPhone until it's finished installing
I've since followed these steps and have not gotten the BSoD anymore. One nice side effect from installing one App at a time is that the new App fills the hole in the icon grid left by the previously updated App. When you Install All, the iPhone will put all the new icons at the end of your icon pages, leaving behind gaping icon holes.