What actually caused the wifi issue:
If you have a new iOS 6 install, you may have experienced a temporary WiFi outage this evening. The problem seems to have stemmed from an unavailable Apple webpage. According to Steve Streza, iOS 6 pings a test URL.
When the web page at that URL went down, so did WiFi access. This URL is meant to allow captive portal network detection at venues like hotels. The problem seems to have been resolved on Apple's end, and WiFi access is, as far as we know, restored for iOS 6 users. If the problem persists, you may have to toggle Wi-Fi off/on on your iOS device.