Proof of Stake is often considered as the successor of Proof of Work (and even more with ethereum 2.0), because of it's more scalable and energy efficient. But there's also problems...

Nothing-to-stake security problem

A part of PoW security is that a cryptographic hash can only be used on one blockchain, because of it's correlated to block data. But on PoS, we only need for balance, and it can be used on different forks. Within a nothing-to-stake attack, the attacker will create a parallel chain (a fork allowing him to "duplicate" his balance) where he's the only one to mint blocks. Then, he produces enough blocks and broadcasts them. 

Loss of "energy-pegging"

A big quality of PoS is that it's energy-efficient, but it's also the cause of this problem. Because of a PoW coin is backed on energy costs needed for mining it, it prevents it from going too low. So allowing to mint coins without energy spending might increase coin inflation.

It's also why some coins (like this good old gridcoin) use an hybrid system (gridcoin validates blocks using PoS and computing power is used for research). 

Increased unequalities

When coin holdings determinate block generating capacity, it makes rich people control a big part of the network, and leads into a kind of centralization. If the coin issuer keeps an high amount of coins, it also gives him/her a great (or full if he/she holds more than 50% of supply) control on blockchain.