Well, in the first place, PoS currency MUST use some better blockchain quality function than longest chain rule, by using latter it's fundamentally flawed(and majority of known PoS around are flawed. Nxt uses so-called "cumulative difficulty" function, which is more or less okay though it's better to be replaced with more sophisticated option(details will be published later).

In the second place to avoid grinding, mutable values should be excluded from hit calculation(as in Nxt). This creates other problems(e.g. long block delays sometimes, as in Nxt), but safe.

In the third place, double-voting isn't a problem itself. Read our papers please.

In the fourth place, I would like to see any details on pools forming in the decentralized environment & cheating evidence publishing.