Skimming the site, it looks to me like DNSCurve is more of a transport protocol for DNS records, almost like running DNS over DTLS. This would certainly be a useful improvement, but I don't see where it talks about how the records are authenticated.
It is pushing off the "do you trust (Versign+USDoJ | greatfirewall.cn) to give you the legitimate answer to your .com query" problem. Which is the kind of problem that the Internet is good at routing around but would be bad for it to do so.
E.g., users will (at best) change to alternative DNS systems or (at worst) toss out this hierarchical authority naming concept entirely. Consider how many users simply wouldn't notice if Google started returning IP addresses or proxy names for search results. Or maybe they set up an alternate with their own naming scheme for Chrome, Android, ChromeOS, and everyone with their search bar. (Oh wait, I just Googled it and they already did that and I didn't notice http://www.infoworld.com/t/dns/google-launches-alternative-d... )
If Google does it, then Microsoft must too. And Amazon, and The Pirate Bay and so then we need a protocol for deciding which DNS system the client will use on a per-request basis, and civil-rights-disrespecting governments try to sabotage that too and round-we-go the Internet we know and love is circling the drain.