what if a virus or malware or an adware installs a bitcoin miner and starts mining on zombie machines? wouldn't that be productive?
The mining process validates the transactions. Transactions are grouped in blocks. The blocks are chained in one big sequence and the miners validate the block chain.
Even if a rogue miner validates a block that steals coins, his fork of the block chain will not be validated by honest miners. As long as the computing power of the honest miners is above the one of an attacker, the block chain is safe.
A dishonest, big enough botnet could overpower the honest miners, fork the block chain and wreak havoc in the system.
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The biggest threat to bitcoin is not technical, though, it is financial. The bitcoin market cap is currently of ~ $50M. If people with deep pockets and trading experience figure that bitcoin is a threat to their deadline, they can easily manipulate the market and crash it.
I can think of ways to manipulate bitcoin market with large sums of money, but nothing that would make bitcoin unusable.
In fact, I think such attack would only create a short term volatility spike but make bitcoin market sturdier in a long term.
In first phase of the attack you would pour in huge amounts of liquidity which would attract more people to bitcoin market.
In the selling phase of the attack you would cause a temporary market panic but only for as long as you sell. And if bitcoin market players managed to find out about what you are doing, they would profit from it.
Finally, when you are out of money, the market would return to its normal course.
Simply buy it up and delete the wallet.dat ... bitcoins go poof with no way to recreate (the total number of created will max out with no regard to losses, intentional or otherwise)