This actually encompasses two questions:
1) What can Amazon do?
2) What will Amazon do?
Amazon has demonstrated that they can examine the contents of your Kindle, determine what books you have, share the passages you have annotated without your permission (which ones, that is, not your actual annotations), and delete books of their choosing. It is assumed that they are capable of doing quite a bit more -- that they basically have full remote access to the computer we call an ebook reader.
What Amazon did do was publish a book without obtaining proper rights, and then, instead of doing what they'd do with a paper book -- namely paying the rights owner whatever royalties were demanded -- they did the functional equivalent of sending goons to the buyers' houses to take the book off their shelves. It didn't help that the book was 1984. Amazon deleted the book from legitimate, innocent buyers' Kindles instead of just paying off the author's estate, the way they would have if they'd sold a paper book without proper royalty clearance, and the people who had their books taken from them were, naturally, up in arms. Amazon has said that they won't do that again. Apparently the money they saved by taking back the books they'd sold instead of just paying royalties ended up paying their PR people to deal with the resultant firestorm.
It's also suspected that even when its wireless connectivity is turned off, the Kindle is either listening for a wakeup signal from Amazon, or turns itself on periodically to check with the servers. Presumably this would allow Amazon to do anything it wanted, including completely bricking the Kindle of someone Amazon believed was doing something they didn't like. Have they? Not that I know of. But given that last weekend, the US government shut down 84,000 websites and declared their owners guilty of trafficking in child pornography (they were really after ... 10) I can't feel too confident that a company who can brick my ebook reader won't do it out of sheer stupidity after demonstrating that they will un-sell you a book if they find it convenient.