Not everyone is the world's best speller and even those that are sometimes hit the wrong key and wind up searching for a misspelled keyword. It's human nature and there's no reason why you shouldn't optimize for the most common misspellings. And there's an easy way to target these misspellings without making yourself look like a fool.
Simply create content on the topic that mentions the common misspelling. Use the misspelling in the browser title, meta description and URL. I recommend acknowledging the misspelling in the meta description (as well as in the content) to help validate their search and encourage clicks. This is important because you have a powerful competitor in Google's Did You Mean functionality and display.
You can even dedicate an entire blog post to the misspelling if you want, like I've done on my Used Books Blog.
Here, I've created a post about used boks, acknowledging it as a common misspelling for used books. The post is focused, humorous (or so I hope) and topical.
A more straightforward approach is one used at Caring.com. In this instance, we've optimized for the keyword genzar a common misspelling of a cancer drug.
While it's currently the number one search result, I'd still like to see the misspelling in a shortened browser title. I'd also note that this was a user submitted question to the site. Be sure to check your keyword and internal search reports to identify misspelling candidates.
The increase in mobile searches will likely result in more fat finger searches. So be on the lookout for this easy source of traffic. But at the same time, don't drive yourself crazy finding and optimizing every misspelling.