edit: not to downplay the egregiousness here. just my advice if you want this "fixed"
Jon I know you're reading, read this : http://www.apple.com/legal/contact/includes/copyright-agent.... which will get the offending apps taken down (or you can hire a lawyer to sue Apple, which should be easy because lawyers love to sue companies with billions of dollars in the bank)
Since these folks are often "related" in that the developers that use these sorts of tactics to make a quick buck are related, if you are persistent they will get the message that your apps are a pain to copy and generally will stop, although you may find it useful to retain a law firm to go after them on your behalf.
While I would also suggest the DMCA route, I can tell you that you will experience the exact same effect (no obvious response) observed by the OP.
Anecdotally, I tell friends and family who are new to their iPhone (or Mac, iPad), that they don't need anti-virus, certainly not on their iPhone. They don't need to worry about downloading bad apps from the App Store, Apple doesn't let anything bad in (Android has a history of malware in its app store). It's what they expect from owning an Apple device.
I really don't want to have to start telling them, "Careful, you could be downloading a fake app" anytime soon. I believe Apple should work harder to stop apps like these from getting into the store - it's much better for developers and consumers.
At that scale they can not "guarantee" safety. The same goes for any other application store, that works at the scale.
Some of the checking the submitter did could easily be automated and flag a user if there is a possibility.
But they "must" be using some tech like that, I hope?
The only reason I found out about them was that in all three cases, there had been some extra resource files included for some unknown reason (likely from another app), which for a very obscure reason were causing the app to crash. I was receiving hundreds of emails containing crash logs and noticed that the process name was different, which is what tipped me off. The fact that all three had the same set of extra files (and all said "Document master" in the modified documentation file) suggested it was either three developers working together, or one developer with three separate accounts.
I found it extremely difficult to get this problem addressed. I contacted Apple and was asked to fill out a form on their website about the apps, and then their legal team just sent an email to the other "developers" asking if they owned copyright. None of the developers responded, and the legal team did nothing. Several more phone calls to the developer relations team left the problem unresolved.
I only managed to get the copies taken down eventually when I was at WWDC and took the opportunity to meet in person with two representatives from the app store team and show them the original & copies. They immediately recognised it was a clear-cut case, and removed the infringing apps within a couple of days.
I think there are some very straightforward technical solutions to this - the submission process could take hashes of all files in a new upload and check them for matches in a database of hashes of all files from all apps, with any matching apps flagged for further inspection. It amazes me this isn't done, especially given the reputation the app store has for being strict about political/sexual content etc. I've seen a ton of copied apps on the store; it's just ridiculous.
Someone else made a comment here about Apple not wanting to get in the middle of copyright disputes (particularly for cases that aren't so obvious). So that's probably why they don't have a process in place to have someone actually look at the apps. Developers have to chase it up themselves, which is annoying.
I'm not sure what the follow up was as I was only there a few weeks, but its shocking how lazy people can be when cloning something.
You can easily browse any native app on a Mac by just ctrl+clicking it and selecting "show package contents"
These cloners are just replacing image files and changing some text in config files which requires almost zero programming or reverse engineering skill.
It would be a bit more code, but just a few lines of verification code when the application launches and the app can refuse to start up if the value doesn't match.
Someone dedicated would still be able to crack it, but it would at least require some effort on the part of the fraudster
Sending an DMCA complaint to Apple/Google has at least the potential to be successful. Trying to take down a web site in Russia or China that is selling your software is another story.
The "developer" also has the audacity to charge nineteen dollars for that particular application. Disgusting.
Also, beside that, people also clone stuff NOT in the iTunes, and I mean clone by literally get someone app for other platform, reverse engineer it, and compile again for iOS and launch it as it was their own (even if controls end being shit).
Given that they provide the sole means of performing this infringement (given that there are no other means to make money off iOS applications), this argument is a bit too generous towards what is basically Apple not giving a shit about developer's rights.
They do not "avoid being involved too much in policing other people's IP"; they are providing the only infrastructure and act as payment processor (even taking their share!) of the infringements taking part. This is morally significantly worse than Pirate Bay and the like (who provide a service to the public), but unfortunately, there's no RIAA/MPAA equivalent for software developers.
 It's debatable whether this is actually unfortunate for the general public
It's in Apple's best interest to project a quality image in the AppStore. Quality over quantity.
They still allow the description and "What's New" text to be changed even after review.