Why isn't my rented movie playing on my iPad?

Try closing the Videos app via the iPad’s taskbar and see if it plays when you re-open it : double-click the home button to open the taskbar and then swipe or drag the Videos app's 'screen' up and off the top of the screen to close it, and click the home button to close the taskbar.

If it doesn't then you could try a soft-reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.

If that doesn't work either (and other videos play ok in the app) then try the 'report a problem' page to contact iTunes Support : http://reportaproblem.apple.com

Or you can try contacting iTunes Support via this page : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption

This advice is somewhat incorrect. Holding the Sleep & Home Buttons is actually a hard reset, not soft. To reboot, hold down the sleep/lock button. You should only hard reset when the unit is unresponsive. Rebooting allows the unit to shut down elegantly. Sleep and home button is equivalent to CTRL-ALT-Delete on Windows.