Gnosis is not needed to answer this one, as it's a very weak claim. There will only be a handful of denominations (maybe one for each order of magnitude?), and one can only guess a given spend came from someone who has ever contributed to the pool of that denomination. As the number of people who contributed to a denomination only increases with time, the likehood the blockchain can be analyzed based on that information only decreases, rapidly becoming negligible.
There will be 24 possible denominations for 10^e and 5*10^e; I expect only the very highest several denominations will be used in the beginning. The Zerocoin GUI will show the number of coins accumulated for each denomination and the mint/spend volume over the last 100 blocks or so, allowing users to decide for themselves how anonymous their ZC mint/spend activity will be.
Relevant code: https://github.com/Anoncoin/anoncoin/blob/zc/src/zerocoin/Coin.h#L26
Gnosis, would you consider dropping the "Zerocoin" terminology, in the UI only, as it's not easily understood by newcomers? For a new user, it looks like there are two separate coins, Anoncoin and Zerocoin, which adds to the confusion. How about just calling them "vouchers" in the client? It's an existing, neutral word with a self-explanatory meaning.
In the future, I'd really like to see an anonymization wizard that entirely drops the need for a new user to understand or deal with Zerocoin, while leaving the possibility for advanced users to do so.