Invalid postback or callback argument after .NET Framework 4.5.1 Security Updates

After the recent security updates of .NET Framework 4.5.1 one of the pages of our website started to throw
"Invalid postback or callback argument. Event validation is enabled using in configuration or in a page. For security purposes, this feature verifies that arguments to postback or callback events originate from the server control that originally rendered them. If the data is valid and expected, use the ClientScriptManager.RegisterForEventValidation method in order to register the postback or callback data for validation."

The website is not in a web farm. The problem can be reproduced on both Windows 7 dev machines and two Windows Server 2008 R2 installations.
In the web.config we have 
<compilation targetFramework="4.5"> Adding 
aspnet:UseLegacyEventValidationCompatibility  makes no di ...