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.