Fresh install of iOS 6.0.1 apps constantly crash
While I have had no problems with IOS 6.0.1 installs on the iPhone 4 and 4s in my household some generic troubleshooting steps would include:

NOTE: back up your phone with iTunes before doing any of this!


Hold down the top button until the phone prompts you to power it down. Do so. once it is off hold down the top button again till it powers back up.


failing that...


Hold down the top and home buttons until it just turns off (ignore the prompt to shut down normally). Once off power up and try again.


failing that...


I heard a while back that if you have THREE power downs in a row (as in #2 above) the phone does some major housekeeping on the third time booting up. Not sure if that is true but on a couple of occasions doing three in a row on my iPhone 4 fixed an issue. So do #2 above three times in a row and then test for symptoms.


failing that...


Attach the phone to your Mac/PC and when iTunes comes up, click on the iPhone in the side panel and then click on the RESTORE button. That will wipe the phone and then restore from your backup.


failing that...


Take it to an Apple store and ask a genius.