Yes, it's worth it. Of course, it depends on how often and how much you type, but for the most part, you'll be happy with the skill.
Not only will you be able to type faster, but you'll be able to keep your eyes on the screen. This also means that you'll be able to transcribe a lot faster. Imagine having a large text written out by hand, and constantly having to look back between the paper, keyboard, and screen. But if you can touch type, your eyes stay on the paper and you trust your fingers to do their job.
As for mistakes and typos, in my experience, there are less to be had with touch typing. And in the event that you do make a mistake, you'll usually feel it right away, and backspacing the right number of characters will quickly become a speedy reflex that you don't even notice.
If you're a writer, and you're on the computer a lot, I definitely recommend learning to touch type.