I was having the same problem the day of the upgrade -> would try to open all new apps and they would flash and then just close out to home screen. What i ended up doing and what has worked - is go to general settings > Reset > Reset All Settings.
You won't lose important stuff (voicemails, SMS, music, notes, etc) but you will have to reset the silly things like favorites, location for your weather icon, etc. It did work, at least for me.
Now if anyone could help with with the SplashID app it would be greatly appreciated! I can NOT get it to work! I downloaded the $9.95 iphone app. went to the website and purchased/downloaded the $20 desktop for OS X, ran the install, dragged the icon to the applications folder. Try double clicking to open and the icon jumps once and then doesn't open, not even at all. Can't get to a point where i can enter my registration key, etc. If - on iphone - i go to tools, sync - it says it can't find the desktop versions...help!@!!!!