All purchases are considered final, but you can try contacting iTunes support and explain what happened and see if they will refund or credit you : 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
If you haven't already done so, then to try and stop it happening again you can turn off in-app purchases via Settings > General > Restrictions > In-App Purchases 'off', and you can set 'Require Password' to 'Immediately' on the Restrictions screen (the default is a 15 minute period during which it doesn't need re-entering).
Sound like he also did an in app purchase for some sort of upgrade. Doubt there is anything you can do on this one. Lots of games are "free", but if you want more thanjust a couple of levels, or the good power-ups you have to buy them through the app. Very deceptive up front so you have to pay close attention.