I acquired my Verizon iPhone less than two weeks ago and had the same problems reported here - many, many "...Application not installed because it is not signed" errors. On following the Apple Troubleshooting advice, iTunes deleted everything I had downloaded on the iPhone.
After reading this thread, I turned off my network card and then turned off Zone Alarm. This time, everything sync'd on the first try.
Yes, it ***** to have to do that, but you don't have to REMOVE your ZoneAlarm; just disable it temporarily to get the sync done. It is a pain, yes, to not be able to use the computer to connect to the Internet for that 15 minutes or so, but if you do it right you won't be at risk and you'll be able to back up your phone/load music and etc.
Until ZoneAlarm fixes itself, this is our best option.