There are a lot of bloggers talking up how to get a refund from iTunes. Most of them suggest you click the "report a problem" link in your purchase history. This didn't work for me. Apple never responded, and then the system won't allow you to click the "report a problem" link a second time. To get a response, I had to submit a request manually via this webform. Make sure to include your order # and explain why what you bought isn't working. Be explicit and ask for a refund.
In my case, I had purchased Slingplayer Mobile for iPad, only to find out that it doesn't support my Slingbox -- even though Slingplayer for iPhone supports it -- and the requirements section of the new application is poorly worded, suggesting that it works with a Slingbox Pro, which it does not. (It actually refers to support for a Slingbox Pro HD, not a Slingbox Pro. The app store ratings page for the application is filled with people who ran into the same issue I did.)