I am getting a band of fuzzy, pixelated stuff running across my screen. What is going on?

It's hard to say what it could be, but try rebooting your iPad and see if it goes away.

Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up

If that doesn't work, maybe you can provide some details - what you were doing when it first happened, when does it happen and so on.

If it comes back after the reset Make an appointment at an Apple Store to have your device examined by a technician. Or contact Apple Support.

I agree with Ralph that it should probably be seen by an Apple Genius, but on the odd chance that some app is corrupt on your iPad and causing this behavior for whatever reason, you could try closing all apps in the recents tray and see if it goes away again. When you start launching you apps again - if the behavior returns - you might be able to pin it down to the most recently launched app as the culprit.

It's a long shot, but you never know.

Sure. This is how you close apps from the recents tray. The overwhelming majority of these apps are not running, but every once in a while, one of them could act up if the apps has corrupt data in it, or of the app it self is problematic. For instance if it crashes on you with some regularity.

Tap the home button once. Then tap the home button twice and the recents tray will appear at the bottom of the screen with all of your recently used apps in it. Tap and hold down on any app icon until it begins to wiggle. Tap the minus ➖ sign in the upper left corner of the app that you want to close. Tap the home button when you are done to stop the apps from wiggling. Then tap the home button again.

Not normal. Take it to an Apple Store for evaluation.

Make a Genius Bar Reservation

http://www.apple.com/retail/geniusbar/

 Cheers, Tom 😉

Just got back from the Genius bar with same problem. Diagnosis.. internal electronics failure. In this case probably old age... it was an ipad 1. They offered an unwarrented repacement for $249... but for an iPad 1 nah...