i had the same problem after the recent update. my non-apple apps would start to launch... and close a second later. phone not jail-broken... a bug on apple's end for sure, or with an app i got from the iphone apps store..
i plugged my iphone into my Mac and it didn't show up on the desktop. i had to launch itunes... and muck about.
i click on the 'automatically launch itunes', started to restore, then backed out... then backed up 'bought' (not really bought, but whatever) applications.
after i ejected the iphone all the apps launched properly.
but the phone is noticably, and at times painfully, slower than it used to be.