There are claims that Apple should not be able to hold the trademark rights to "App Store" since this phrase has become a generic term.
In a 27-page filing Microsoft argues that "'App' is a common generic name for the goods offered at Apple's store, as shown in dictionary definitions and by widespread use by Apple and others" and that 'Store' is generic for the 'retail store services' for which Apple seeks registration." Since the App Store is in fact a store, the complaint is well-founded, Microsoft said. We have no idea what the final decision on this matter will be and it may all depend on the weather and the mood of a judge to be victorious in this battle.
However, since we know that you can patent virtual everything in this country, and companies have become so bold that they are even trying to patent the essential idea of holding a patent we would not be too surprised if Apple in fact could get the trademark confirmed. It almost sounds silly if a company claims that a certain claim in a trademark or patent is generic. Was it Microsoft that patented the OS shutdown last year?