OK this might seem a little dumb but the Paddy Power iPhone app page on iTunes says the app required version 3.0. I haven't upgraded my iphone OS since I bought it a couple of years ago. How do I check that I've got the required version of iOS?
Unless you iphone is really ancient you should be OK. Most iphones are up to 5.x by now. If you do want to check what version you are running just select the "Setting" icon from the iPhones home screen. Then scroll down until you come to the "General" option. In there you should find the "About" option. My guess is that you're probably running 4.x version of iOS.