Thanks bhz1. During my trials and tribulations, I had already deleted the app from iTunes and redownloaded the latest version with no help. Also, I'm fairly sure the AppStore iPhone app always downloads the latest version. Also tried deauthorizing/reauthorizing from the AppStore and all those crazy things.
Unfortunately, the problem remains. Anything / everything else appears to work correctly. I've tried reinstalling already purchased apps, buying new apps, etc without issues. I'll bet there is a dependency conflict -- like a Cydia app that installed something AirShare needs or wants configured differently (???) In truth, I have no idea. Just rambling.
Once this problem is discovered --- it'll probably be obvious.
Hey --- is there a way to rebuild the 'AppStore' installed database? Or some other tools that could attempt to clean-up iPhone errors? More rambling here ... except for the unusable 0xE00002e (unknown error) message.
Oh yea, maybe a syslog file can shed some light on this? Maybe you / someone could direct me towards the log files I should look at?
Thanks in advance.
Edit: Had another thought ... try to install a prior version (like 1.0, or 1.0.1, I save everything

) -- current is 1.1.1. But iTunes doesn't recognize the prior version -- even if the latest is deleted. Is there a work-around to install prior and authorized/legit Apps?
UPDATE 2222 (haha): In absolute desperation I completely removed AirSharing from iTunes and sync'd. Everything appeared normal. Unfortunately, when updating 'any' application from the iPhone .... that app IS updated BUT I also get the following error message:
"Unable to Download Application -- Air Sharing will be available for download when you log in to the iTunes Store on your computer. Done and Retry Buttons."
The iPhone is trying to update AirSharing forever. And since the 1st upgrade 'error'd' the app is no longer installed. It was deleted from iTunes and sync'd ... but not the iPhone. Also ... WinSCP/SSH now report about 4 or 5 instances of the AirSharing hex-crazy-name folder. Eventually, my system will run out of space ... and break something else.
Any suggestions?