Flaws I see in the white paper:

1. Non-zero transaction fees.

2. PoS, i.e. does nothing to deal with centralization of mining.

3. The anonymization is flawed. It relies on two mining nodes not sharing their knowledge of which transactions correlate to which inputs received by the network. That is a fundamentally flawed concept that I dismissed long enough with my analysis of DarkCoin, because mining nodes can be Sybil attacked (the adversary can flood the network with mining nodes). It gets worse with PoS because those with the largest stake have the most mining nodes, thus your anonymity is for sale (or hackers can target with spyware those nodes with the highest stake).

Worse yet, if the first peer of the two has seen the transactions then it doesn't matter how the second peer rearranges them, so the entire thing is trivially defeated.  Assuming the senders of the transactions are encrypting them for the final peer, then the problem is as you add stages/hops (the paper proposes to double the stages) the system can be attacked with transaction spam since the transactions aren't verified until they are decrypted at the final peer. I assume you could ban IP addresses if sending nodes can't enter the network at-will.