I had over $2800 in inadvertent in-app purchases back in November/December of 2011. The resolution should be easy enough through the Apple Support site (by going into your own account on the itunes store and clicking on the purchase to "report a problem"). I've read of many people getting refunds if they go through sending a request for refund for each and every purchase.
I took a different route since I wasn't getting the desired response from Apple -- they definitely pushed back on it and told me how to disable in-app purchases to avoid future mishaps, but weren't indicating that they would be willing to refund the money.
When I didn't get the immediate refund I had hoped for, I contacted my credit card company and disputed the charges -- I did tell the credit card co. that they were from my son gaining access to my account without my permission and making the purchases without my knowledge.
They did what is called a "charge back"; and credited my account while taking the money back from Apple. Once I initiated this, Apple would only work with my credit card company, and after some time, Apple agreed that I did not have to pay for these charges.
I did get a full refund. It was resolved within a 45-day time period....and the money was credited back immediately from the time of my phone call to my credit card co. The credit card company investigator told me that I can always request a refund and should be issued a refund from Apple for the simple reason of being "dissatisfied with my purchase"... either that the value of it wasn't worth it or I didn't like the app or the in-app purchases and found it lacking in entertainment value. That alone is reason enough to want and get a refund!
I would suggest that you take the time to enter each charge and tell Apple that they were "unwanted purchases" and you would like a refund -- do this via the support website.
I've heard more and more cases are now being resolved in this manner.
If you can't get anywhere -- then call your credit card company and complain -- the major credit card companies have some awareness of the issue and have been working with iTunes and the various apps that offer the option of in-app purchases targeted at young children.
I've heard things like, Class Action Lawsuit bantered around -- in other words, you absolutely positively should get your money back, and if you're persistent enough about it, you will be successful.
I went so far as to contact Pocket Gems, Inc., the makers of Tap Zoo and other apps where the charges were racked up by my son. Pocket Gems support agreed to work with Apple to issue a refund -- but since I'd already begun to work with my credit card company, Apple didn't even want to talk with me any more!
Don't give up -- you'll get the refund eventually!