It solves the nothing at stake problem by comprising through it necessitating trust in some third party entity. The third party in this case is the community and it's elected witnesses. Witnesses certainly have something to lose if they misbehave, but if the community doesn't really care a lot about the witnesses then witnesses may be able to get away with some things. We trust that enough people care.

The current blockchain is vulnerable to voting collusion among whales (less than 51%) and general apathy of the majority of the users (some significant %). There are certainly small fixes that we can use to make it more secure, but that flaw with always be there. But hey, it might be worth it for such a fast and expansive blockchain.