First hand, I only have experience with the iPhone / iOS devices.
I had run across a review on the Kindle Fire at TechnologyRight (he had linked to one of my articles, and I was checking out his site). He mentions that it is too easy to buy content on the Kindle Fire. Definitely a problem (especially if you have kids, as John mentions).
One minor annoyance for me, is how I have to put my password in every time I want to buy, update, or sometimes use content on my iPhone. It is 2012, can we not decided whether to remember our password or not? It’s too hard to buy something. If I want to, let me click on everything and pay $0.99 every time I make a mistake. I want that option.
Personally, being without kids, it would be great to be able to hit “Update All” and not have to enter a password. After all, we can password protect our devices.