People are probably not going to like the suggestion, but when an upgrade results in bizzare or unwanted behavior, the easiest, or perhaps even the only recourse may be to perform a Factory Data Reset after backing up your phone's storage to a PC, and copying down important settings for things like email, or online banking, etc, or just copying down what apps you downloaded and where you stuck icons.
Sometimes an offending program can be identified, perhaps uninstalled and re-installed, or perhaps it's cache cleared, and then it behaves, but not always.
I think upgrades are meant ideally to work and leave you as you were but with an updated OS. But it's possible, some programs, processes end up referencing memory that's not initialized properly, and only by doing a FDR is the phone set to a state that is deterministic. There are simply too many variables on what has been downloaded, installed, uninstalled, etc across the user base on all devices, and simply too much complexity to guarantee 100%success for all users, all devices.
Personally, in the past, having multiple phones and experiencing multiple OS updates, maybe 60-70% happen without me having to perform a FDR. I'm lucky this time with KK, but others have had problems, and FDRs have generally cleared those problems. The 30% of the time I had to do an FDR, the results were satisfactory, but I did have to do some work to get my phone back to a state I had it configured previously, and I know that isn't fun.
I bet this is what VZW or LG are going to tell you to try. Backup your photos and your music and other downloaded content that is important to you. Capture your account names. I think if you had it set properly, your contacts should be backed up on Google's servers.
