How do I record a screen cap video of the iPad?
Reflection (US$15) turns a (Lion or above) Mac into an AirPlay receiver that can handle mirroring.  Once you've got the mirrored display on a Mac, all you need is to capture that video, which is easy.

For example:


Start Reflection on the Mac.
Turn mirroring on (requires iPad 2 or newer or iPhone 4S or newer), selecting the Mac as the target.
Use a video screen capture program (Quicktime Player can do this, but there are lots of more advanced ones if you need more) to record the Reflection window.


No jailbreaking is required.

AirServer (also US$15) is another application that offers essentially the same functionality as Reflection (and was released slightly afterwards), but is also available for Windows, if you don't have a Mac to do the recording on.