Quote from: Rannasha on December 02, 2013, 11:00:37 PM

Changing the payout address in a newly mined block requires redoing the proof-of-work.

Ah. The hashing info is calculated taking into account the payout address?

Found this https://en.bitcoin.it/wiki/Block_hashing_algorithm So the block header is comprised on the following components

Component Reason Updated
Version        Block version number        You upgrade the software and it specifies a new version
hashPrevBlock      256-bit hash of the previous block header     A new block comes in
hashMerkleRoot     256-bit hash based on all of the transactions in the block     A transaction is accepted
Time     Current timestamp as seconds since 1970-01-01T00:00 UTC Every few seconds
Bits     Current target in compact format     The difficulty is adjusted
Nonce        32-bit number (starts at 0)     A hash is tried (increments)

So a transaction is verified if it makes sense based on the nodes blockchain, it is then added to the blockchain and the merkle root is recalculated(?).

When someone is mining, do they add the transaction that pays them out to the blockchain they have, changing the merkleroot, and then hash it and broadcast it? This way someone can not change where the payout goes to without rehashing/doing a crapton of work.

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Seeing as that fails, what if someone was still able to gain control to all of the nodes one person is connected to?

I guess the most they could be is an annoyance.
They could just not broadcast new blocks to the node, and send it random transactions (generate tons of transactions to and from themselves). If this is done to a node that holds a considerable portion of the networks computational power though, it would weaken the network making it easier to perform a legitimate 51% attack.