I've been (also) experiencing issues since my Galaxy S3 was pushed the 4.3 update on the morning of 1/11/2014. The worst is the battery drain - losing more than 50% of battery life within 4 hours of 100% with only minor texting during that time - with the charging process taking nearly 3 times longer to fully recharge. The moment it's removed from the power cord, it drops to 98%. This was not happening before update.
Today, I called Verizon's technical support who recommended a factory restore. Since I read endless posts/experiences of this not resolving the issues, I chose not to take that path and to work with Samsung to understand when a fix would be pushed. After 45 minutes on the phone with Samsung explaining the issues as if they'd never heard of such problems with the update - I was told that I clearly had water damage to my battery which was causing all of my issues. Sure, and everyone else who owns an S3 in these forums has the same water damage. Of course, the moment I asked to speak with the Samsung rep's superior, our phone connection grew dim, sputtered as if it were a bad mobile connection, and suddenly disconnected.
I experience the "Unstable Internet Connection" to WiFi when no other phones have issues with these networks. They're the same networks I've always used - but since the update, they're now "unstable".
The lag to wake up when I receive a call or text sometimes takes 10 swipes and a few freezes before it finally unlocks.
I've downloaded no new apps since the upgrade, yet apps I used regularly prior to the upgrade now randomly freeze on me, requiring me to remove the battery to restart the phone.
Unless Verizon is willing to let me out of the 2-year contract since I'm not able to use my phone in the manner to which we'd agreed in that contract, they had better start acknowledging a large-scale problem with this update and work dilligently with Samsung for a speedy resolution. Just seems odd that this update was pulled back in November for these exact issues, yet Verizon chose to allow it to be pushed to their S3 users in January without resolution from Samsung. Gee, wonder if it's so we'll all upgrade to the S5 as it's release is a few months off. Hmmmm.