Pros
The company is growing and has recently increased the research staff significantly. Amazon is also unique in the size and scale of its operations from AWS to retail supply chains - you get data and problems that are an academic's dream. The company is result driven, and there is a high pressure, but you learn a lot about things you would never imagine from outside. In my time here, I have worked on cutting edge research to writing terrible code that has been deployed across the company. If you get on a good research team or important project, you can have a huge impact.
Cons
It isn't really a research company - the typical academic (work on projects for months on end with no actual product) might find it a huge disappointment. There is no publishing mentality. Working on cutting-edge ideas is not encouraged if a heuristic or rule based approach is "good enough". Fancy theory doesn't impress anyone and doesn't give you credit unless it gets in to "production". The infrastructure for research are bad. No access to journals and papers, no cleaned up and pretty data sets. You have to write database queries against an aging database that the whole company is fighting for time with. If you join a team with a lot of researchers, you are in luck. If you join a team as the sole researcher, your manager might ask you to plan "agile" research scrums. The pay isn't enough to justify spending your Ph.D. on mundane projects. The company nickle-and-dimes you for everything, and benefits are almost non existent.