After mining the hash value for the new block, How many nodes can confirm the correctness of the hash value by miner? In one of blockchain paper, all other nodes must mutually confirm the correctness of the hash value. I think that it is impossible to all other nodes can participate in confirming the correctness.
Yes, all full nodes validate all blocks. Not only do they validate the hash is correct and meets the current difficulty requirement, but they also validate that all transactions in the block are valid. This means they also run all the smart contract code that was executed in the block.
All of this is a very small amount of work and prevents a node from operating on an invalid blockchain.
Just to add to @smarx's correct answer:
The main thing to realize is that mining (finding the right nonce or answer which fulfills the PoW "puzzle") is very difficult and requires a lot of processing power. But verifying the result is trivial.
To verify that a given nonce is the right answer for the PoW work the verifier simply needs to execute one hash calculation which is very cheap to do. Miners have to execute millions of these calculations to find the right answer.