Symptoms
Customers enter payment information, go to the checkoutreview page and click "Place Order", and are sent back to the checkoutpayment page with the above error message.
Cause
This is caused by a change in functionality of the .NET framework introduced in .NET version 3.5 Service Pack 1.
Solution
Open the checkoutreview.aspx page and find the following line (around line 24):
<form runat="server" action="checkoutreview.aspx">
And change it to:
<form runat="server">
Checkout should now function normally.