What methods are there for making a screencast from an iPad 2 or 3 with iOS 5?
Reflector App

I have purchased and evaluated a newly released program called Reflector App (which runs on your Mac) that does everything I need it to do. It costs US $15 and works using Apple Airplay on your iOS device, so it supports iPad 2, iPad 3, and iPhone 4S. It makes its own QuickTime recordings with audio and video. If you have a good connection with a WiFi N router (such as my Apple Time Capsule) and an Ethernet connection to your Mac, you get a frame rate good enough to record yourself playing Angry Birds, at full iPad screen size. It records audio and video from your iPad.

This app is quite new and small updates are being released frequently. The documentation is sketchy but the tech support via email is responsive.

You can download a trial version that will only work for 10 minutes total; after that you must pay for the app. It's not available in the Mac App Store and I suspect it won't be. You can purchase it directly from the web site.