Which should we work on as the unsolved problems in cryptocurrency and why?
Scalability - Increasing transaction processing capacity and speeds on blockchains to support wider adoption. Issues around block size limits, transition to proof-of-stake, sharding, layer 2 solutions.
Bitcoin can solve its scalability like in 2017 but I believe the community will not increase it too much. Each successful scaling up round will be a big news for Bitcoin and it's good for Bitcoin bull run. With this motive, I don't think reasons to increase the block size to very big that will not require any upgrade for next 12 or 24 years.
Layer 2 solutions, Bitcoin has Lightning Network to do off-chain transactions with small transaction fee, in satoshi.
Proof of Stake is for centralization, that is not what Bitcoin needs to move to. It's the only cryptocurrency that has a decentralized network and decentralized distribution.
Sharding is for Ethereum blockchain and EVM blockchains.