The fundamental problem is that stakeholders can mount double-spending attacks effortlessly.
I'm not convinced of that. True, they didn't release much information on this, but to me it looks like you only have the chance to use your stake to mine a block once in a blue moon.
It doesn't matter that it's rare. You can get access to a steady flow of double-spend transactions via a kickback mechanism:
You, a wealthy hacker, would implement a "ppcoin-double-spend-edition" client. It works exactly like a regular client, except there is an additional "double spend lottery" button. When user clicks that button client creates a double-spend transaction for a recent user's transaction and it submits this transaction to you.
This double spend txn will spend 90% of input to user and 10% as a kickback to you.
Now I assume that this client will get popular since users have a chance to buy products for 10% of their cost.
If this client is popular, you get a constant stream of double-spend transactions with kickbacks to you.
You include these double-spend transactions into your proof-of-stake blocks, aiming to trigger a reorg. If you successfully mine it and reorg is successful, you earn kickbacks. If reorg doesn't work, you lose nothing since your coin-days are not consumed and you can try again.
Alternatively, you can use proof-of-work and send-to-self to increase coin-days consumed in your transaction. Quote from the ppcoin paper:
The protocol for determining which competing block chain wins as main chain has been
switched over to use consumed coin age. Here every transaction in a block contributes its
consumed coin age to the score of the block. The block chain with highest total consumed
coin age is chosen as main chain.
Apparently, it doesn't matter whether coin-days are consumed in proof-of-stake blocks as a stake or in proof-of-work blocks in transactions.
So you can mine proof-of-work blocks which include double-spend transactions and aim to do a reorg. You can easily check whether it's currently possible and how much of an opportunity do you lose in terms of interest and power spent on hashing. Thus you mine only when there is a chance of profit, and on average this operation will be profitable.
Even if you own just 1% of hashing power you have a chance of double-spend once in 100 blocks, which is significant.