> With proof of stake, nothing is preventing you from 'mining' on multiple base blocks on the same time. Anytime you spend a coin and get the goods, you might as well try and see if you can 'mine' 2 new blocks to erase your transaction.

Ethereum's proof-of-stake approach appears to solve the "nothing-at-stake" issue, see the Mauve paper for more details: http://vitalik.ca/files/mauve_paper.html

TL;DR of their approach is that if you mine off-chain blocks they can get later-on included by other (PoS-)miners via the "dunkle" mechanism. If this happens there's a penalty for the original miner who mined a block that didn't make it into the current chain.