One thing I haven't been able to figure out about proof of stake is this: if one entity somehow manages to control over half to the total ETH tokens, does this enable an attack analogous to bitcoin's 51% problem (which happens when one miner controls over half of the network's raw cpu power)?
No. The required amount is greater than 2/3 (67%) not greater than 1/2 (51%) on PoS for Ethereum. Also, see this tweet from Vitalik: https://twitter.com/VitalikButerin/status/130129808602782105... So even if there was a successful first attack from some organised body that's all the time they get.
I'm not sure that's correct (the tweet doesn't get into any details so I went to ethereum's website https://ethereum.org/en/developers/docs/consensus-mechanisms...)
> The threat of a 51% attack still exists in proof-of-stake but it's even more risky for the attackers. To do so, you'd need to control 51% of the staked ETH. Not only is this a lot of money but it would probably cause ETH's value to drop. There's very little incentive to destroy the value of a currency you have a majority stake in. There are stronger incentives to keep the network secure and healthy.
The keypoint seems to be that if your attack fails your stake gets destroyed so besides the positive incentives (a good stable network working for all) this system also relies on punishing failed attacks.