If a miner with double spent or change of the old accounts or prints money nodes doesn't accept it.
Certain type of double spend is still possible. For example, 51% attacker deposit 100BTC to exchange. But after it receive 6 confirmation, the attacker overwrite 6 most recent blocks with different ones which exclude TX used to deposit 100BTC to exchange.
So the hashrate produces a fork yet normal good ones continues the good one. Is there anything wrong in this?
Even while following all Bitcoin protocol, there are harmful things 51% attacker could do. For example, mine empty block where no TX can be confirmed or intentionally exclude certain TX/address from block they mine.
- The mining pools can simply use different addresses for each new block they mine, so that no one can estimate their hash rate.
In addition, the attacker also could fed false data on Coinbase TX in attempt to make confusion.