This post is a result of two things.
a) all the plagiarism that's going on online
b) reading through old reviews that involved unfortunate implications on the part of the author
There are many different ways people apologize--explanations, excuses, promises not to do it again. Whatever your method of choice is, there's just one thing you have to remember:
An apology is not about you. It is about the person you wronged.
The purpose of an apology is not to defend yourself or to win back the favor of your readers or the person who's mad at you. If that is your primary goal, then you are not really apologizing.
The purpose of an apology is to acknowledge that you did something wrong and that your actions hurt someone. Think about it from the other person's perspective. It's bad enough when someone hurts you, but it's even worse if that person fails to acknowledge that you were wronged in any way. If you, the offender, are disregarding that person's feelings, then you are not really apologizing.
I also want to add that part of your responsibility to the person you wronged is to make sure that person doesn't get harassed because of your actions. You may think your fans are kind, intelligent people, but loyalty can make them do stupid or even cruel things. Beautifully Invisible, the blog that was plagiarized by The Story Siren last year, discusses how she was harassed by some of The Story Siren's defenders. Had TSS devoted one sentence of her "apology" post to asking her readers not to harass the other bloggers involved, that mess could have been prevented.
But how does this relate to book reviews?
I'm sure we've all seen cases where authors fail to apologize for offensive content or glaring errors in their novels. Remember when P.C. Cast failed to acknowledge a reader's anger over the word "retard" in her book, and then used her next book to defend herself? Or the way E.L. James refuses to admit that her books feature an abusive relationship? Or, my favorite, when Christopher Pike used a sock puppet to defend his very obvious research!fail? (yes, I know I've linked to that before, but it never. stops. being. hilarious.) In all of those cases, it would have been very easy for each of these authors to write a blog post saying "Yes, I made these mistakes. I'm sorry. Next time I'll be more thoughtful and less of an ignorant/lazy fuck." Why is it so rare for authors to be able to do that?
And then you get authors who don't even address the mistakes. When I reviewed Origin and Beta last year, I pointed out issues that bothered me, not just in a "this is bad writing" way, but in an "unfortunate implications" kind of way. In Origin, the issue was the author's horrendous misrepresentation of cerebral palsy. In Beta, I was upset by how the protagonist wasn't allowed to get an abortion after she'd been raped. I figured these books must have been out long enough that these authors would have heard people complaining about these issues, and I wondered if they had thought to apologize for them. I didn't find anything. (But admittedly, I didn't look that hard. If you happen to find something where either of them addresses the issue, please link me to it.) And while silence is certainly better than starting an accusation war, it's still failing to address the issue: that somebody was hurt by your writing.
I'm not much of a fan of Veronica Roth's books, but one thing I admire about her as a person is that she's not afraid to admit when she made a mistake. I was especially impressed by the way she apologized for how her personal biases led to her writing Tobias as white, even though he should have been a POC. A lot of whitewashing in books/movies gets brushed off as NBD, and people refuse to acknowledge that the under-representation of minorities might actually have detrimental psychological and sociological effects. It takes a lot of courage, humility, and maturity for an author to actually admit that she made a mistake. Same goes for Justine Larbaliester's great post on racism and Liar.
People wouldn't complain to you if they didn't legitimately feel hurt or offended by your actions or writing. So please, when someone calls you out on a mistake, please examine your actions and think about them before you get defensive. Maybe you can actually learn something.