How can I modify a package from the Mac App Store? I used to hack at apps on my Mac all the time (change the icons/sounds etc... in the resources folder of the package). I have tried with apps downloaded from the App Store, but it no longer seems to be possible. In fact, even creating one empty file will stop the app from launching. I assume that Apple are doing some kind of one way hash of the application folder, and checking if it has changed.

Is it possible to either bypass the code-signing check or be more sophisticated about modifying apps that are signed and downloaded from the Apple Mac App Store?
It depends upon the app. For example, I've been able to replace the icon of djay (bought it in the MAS) with the one from Cyberduck, and djay launches just fine (except it's got a rubber duck as its icon now :-))

If the developer does an integrity check at start time, you're out of luck.