According to posts on Apple’s support forums and Twitter, many of those who have upgraded to iOS 6 are experiencing Wi-Fi connectivity issues.
Based on the claims, the issue has arisen from a network verification process baked into the software, wherein the OS attempts to load a dummy page on Apple.com to detect if a users is connected to a paywalled network.
Unfortunately, however, the verification page seems to lead to a 404 error, resulting in an inability to connect to Wi-Fi for many users…
Annoyingly, I ran into this as I got home this evening.. The problem quickly fixed itself, but still annoying..