I did a lot of research some time back, before I started doing giveaways on my website. This kind of thing is not a gray area. Legally, it could get you into trouble. I'm sure people get away with it, but why take the risk?
In every US state, the ability to hold lotteries is limited to the state (or completely nonexistent). The UK has similar rules, except that select charities are allowed to do lotteries.
What constitutes a lottery (as opposed to sweepstakes, or legal giveaway)?
There are three factors: a consideration to enter, random selection of winners, prize(s) of value. On the first point, the consideration need not be monetary. Anything that takes up enough time could be regarded as a consideration. Asking someone to follow you on Twitter, for example, doesn't take enough time to be so regarded, but asking people to read a book and write a review could easily be seen as a consideration. On the third point, it's true that the prize isn't huge, but it certainly has value. The selection of winners is random. All the ingredients for an illegal lottery are present. That doesn't mean you'd be noticed and prosecuted, but why take the chance?
Then, as others have pointed out, there's the TOS. The only thing you can offer reviewers is a free copy of the book being reviewed. Yes, you could have the reviewers post only on non-Amazon venues, but here's another fun fact. The Amazon TOS on this point is based on Federal Trade Commission regulations. (So yes, incentivizing reviews also carries legal risks.) As with illegal lotteries, how stringently the requirement is enforced could well be questioned, but every so often the FTC does crack down on something. You don't want to be the one that gets cracked.
Though I occasionally see people do things that make me wince, and they don't seem to get into trouble for it, I'm sure we can all agree that it's better to stay on the right side of the law.
