There are times in your life when you're going to put your foot in your mouth. It's inevitable. And I'm hardly innocent in this matter. (I used the word "crippled" to describe a character with quadriplegia. A reader called me on my offensive behavior.)
But it's how you handle the dumbassery when you're called on it that really matters.
You start by apologizing. Not excusing, not back-handed apologizing. A simple apology. Maybe with a promise not to do it again.
WRONG: I'm sorry you were offended.
RIGHT: I'm sorry.
The worst one though is "I was just joking."
Yesterday, I read another blog post that was so sexist that it made me literally nauseous. I protested in comments. The response I got from both the writer and the blog host, both women by the way? The writer was just joking, that she was being ironic. In fact, the blog host went as far as comparing the post to Stephen Colbert.
Um, no. Pointing out hypocritical absurdities in our culture isn't the same as saying Ellen Ripley (starship officer trying not to be used by an alien as a baby incubator) and Annie Wilkes (psycho who delights in cutting off the limbs of her favorite author) are the same type of woman.
In fact, it's all too close to someone making a racist/homophobic/religiously offensive joke, then looking at the offended person with a blank expression. "B-but I can't be a bigot. I have friends who are black/gay/Muslim."
As one of my favorite authors would say, once you've put your writing out in the world, it's up to the reader to interpret your meaning.
If you did your job correctly as a writer, the image in the reader's head will be very close to the image in your head.
If you failed miserably as a writer, well, you're going to get called on it.