Question: Suppose organization X has 51% of the hash power for a period of 1 week. In this week, what exactly can and can't X do?

Answer: 
And then there is the denial of service possibility of suddenly withdrawing from the service, taking the necessary computing resources away to continue to solve blocks every ten minutes until the difficulty is adjusted down again (which could take a long time if there is only a block every day for example).

Of course, for that one would need much more than 51% of hash power.
I suspect he might be able to mine more than 51% of the blocks. See [Can someone with 51% computing power earn more than he deserves?](https://bitcoin.stackexchange.com/questions/1475/can-someone-with-51-computing-power-earn-more-than-he-deserves)