To quickly follow up on your aside regarding how this might work for copyright issues (as opposed to for trademarks): the DMCA procedures do not apply to Apple due to their specific curation: they have forfeited any possible safe harbor protections, and the procedure for dealing with them is not simply a take down notice.
Thereby, if you have an issue with an app in the App Store, you can and probably should (as in, the American legal system will, in the end, fail to work correctly for you if you don't) directly sue Apple for any copyright infringement that occurs in their App Store. (Of course, most directly, what you should do is talk to your lawyer. ;P)
(I am not a lawyer, but I do run Cydia, the alternative to the app store that distributes substrate extensions for jailbroken devices, and have in the past run other systems such as Cyrket. I thereby have received a fair number of C&D's myself, and have had my own lawyers brief me on these matters.)
(That said, Cyrket had DMCA safe harbor and for Cydia I only host my own work, so I can easily and often be fuzzy about details as they might apply to companies like Apple. It is interesting, though, to hear at conferences from people at Google about the balance the Android Market must keep to maintain their DMCA safe harbor.)
I highly doubt that curating the market removes the safe harbor immunity. They are no longer a common carrier, perhaps, but that's orthogonal to the DMCA safe harbor.
I appreciate your doubt, but am having a difficult time matching it up with the law. In specific, the DMCA safe harbor provisions only apply to entities that can be called "service providers", and Apple's prior-to-posting editorial control over the contents of their catalog then seems to be incompatible with the definitions that are laid out in USC § 512. Apple, playing the role of online retailer, thereby seems to be every bit as responsible for the content of their App Store as if they were to be hand-compiling printed catalogs of products for their own mail-order company for which they stocked their own inventory.
In comparison, Google pulls some ludicrous stunts to maintain separation: developers sign up separately for a payment merchant account (yes, also from Google ;P) and are legally responsible for things like their own sales tax collection (yes, this is insane). Google, then, attempts to claim that they are just a mechanism to allow direct-from-developer-to-user sales of products, and that their catalog is nothing more than web hosting. (This also has the horrible side effect, of course, that even if someone at Google has reason to believe something is sketch in their store, they have to not touch it and wait for something to come through channels.)
Thereby, if you have an issue with an app in the App Store, you can and probably should (as in, the American legal system will, in the end, fail to work correctly for you if you don't) directly sue Apple for any copyright infringement that occurs in their App Store. (Of course, most directly, what you should do is talk to your lawyer. ;P)
(I am not a lawyer, but I do run Cydia, the alternative to the app store that distributes substrate extensions for jailbroken devices, and have in the past run other systems such as Cyrket. I thereby have received a fair number of C&D's myself, and have had my own lawyers brief me on these matters.)
(That said, Cyrket had DMCA safe harbor and for Cydia I only host my own work, so I can easily and often be fuzzy about details as they might apply to companies like Apple. It is interesting, though, to hear at conferences from people at Google about the balance the Android Market must keep to maintain their DMCA safe harbor.)