Vantaggi
You have a lot of autonomy and responsibility. You are given a lot of respect for being good at your job... I didn't find much internal politics (even though I've sure it exists elsewhere in the organization). This may be one of the main reasons that Amazon is such a respected name on the the resume. Also, the MBA intern network is great. There were ~180 MBA interns (3x as many as Microsoft) from all the top schools in the country (HBS, Wharton, Stanford, MIT, Berkley, etc). We all hung out together after work, and I've stayed in touch with many colleagues from other schools after the summer.
Svantaggi
As an MBA intern, it's very important to fit a good project. You are evaluated on how well you complete your project and write your white paper, so make sure you pick something where you know what the end result should be. Open-ended projects, where you don't deliver something tangible (like a new web site feature, new marketing campaign, new product, etc.) will most certainly get you dinged during your final review. I had friends who loved their experience, and I had friends who hated it. I think the major reasons people didn't like their internship were: 1) Their project was not well-scoped and overly-complicated, so you didn't know what the end result should be, and 2) People were expecting a culture like Google or Facebook (lots of benefits and perks), even though Amazon is as much a frugal retailer as they are a tech company.