I'm a a new college grad who just recently went through this exact same process, but was turned down after the first stage. The test required webcam, browsing monitoring and location access. It also said it would periodically capture my webcam and exit the test (with no way of finishing) if it detected any loss in webcam connectivity. I didn't have any webcam available for my use so I rigged up my DSLR to upload to an ip cam which I then streamed as my webcam capture. It all worked splendidly except for the fact that my DSLR shuts off automatically after an arbitrary amount of time (something to do with it's idle timer I couldn't fix). Since it was the only webcam I had on hand I went ahead and took my chances with the test.
30 minutes later I had finished the programming portion rather easily, although because it was timed I had to rush on the last problem (write an implementation of insertion sort), copy/pasting code I had written earlier in the test. My webcam was still capturing and I even reset it here in between portions. I then began on the logic portion of the test, basically a glorified IQ test. Now, I work methodically and consider questions from all perspectives - the questions posed were all relatively easy IMO however could sometimes be answered a couple different ways depending upon your logic. I'm not saying the questions were flawed, it just made for a white knuckle situation. I ended up rushing through most of the questions and left 6 or so unanswered. Oh, and my webcam went out halfway through so I spent a couple minutes resetting it (it didn't exit the test like it said it would).
A week later I got an email saying they would not be following up with me. No harm no foul, seems like what I'd been hearing was true; I didn't want to work with a company that interviewed like this anyways.
I just want to say that I was terribly disappointed in this particular interview process; I felt like it caricatured the state of the modern technical interview in all its glory. Not as a whole, but in general. It sifts for people, not necessarily coders, who work well under pressure of a timer. They miss out on candidates, like me, who think critically about each question and take a creative approach to problem solving. But then again, perhaps Amazon is simply being selective on this basis. This process completely cut out the middle man, in fact I never once emailed with a real person about this interview. I was never given an opportunity to demonstrate who I was and how I think. But like I said, perhaps Amazon wasn't interested in that.