The double spending problem is completely eliminated by having unique coin IDs and using digital signatures. The worst attack nodes could do would be to mess up the distributed hash table.
If you can "mess up" the DHT then you can double spend. For example, send some coins to an exchange, trade them for btc, then scrub the transaction from the dht (perhaps via Sybil attack) and send the same coins off to some second exchange and sell them again. Having the coins identified and signed doesn't really help the first exchange.