I have the same issue. It's not as fast as my s2 on WiFi.also sometimes it loses signal and the WiFi turns off by itself and then on. It's really weird
This is my symptom since Day 1 for a Blue 32GB, as well. We've had Droid Incredible and Incredible 2s here, iPhones from 3-4s, a Galaxy 7" pad and an iPad 2 - all work fine with the Wi-Fi from my Netgear WNDR3700 at 2.4 or 5GHz (i.e., I have two channels, different network names) using WPA2-PSK (AES).
Web browsing on Wi-Fi has been horribly slow with many timeouts and I can't even connect to check for a Software Update via Wi-Fi (unless that's normal for such a function).
Will be testing with my spouse's white 16GB later today to determine if it's only my Galaxy S III having problem.
I'm about ready to call Verizon for service, because Wi-Fi performance - even connecting is haphazard - is a big pain.
- ooofest