Someone mentioned in coindesk comments that an anonymous coin is a serious problem because you can't determine if the code has been hacked to generate excess coin. In support of this, I found this in the blog:
Perhaps there could be a way to audit the size of the Zcash monetary base, without compromising the privacy of any users. That way...at at least we can tell that they have not (yet) used it to counterfeit money.”
It seems like a serious problem, requiring faith that Zcash will not be printed like fiat.