LOL, when I got the job announcement for my current position, I think I pounded out the cover letter and sent it off by email within half an hour of getting the announcement. It sounded perfect, and I'd just updated my resume and had a great writing sample ready to go, as well as a link to a video of my then-recent argument before our state supreme court.
Imagine how *I*--writing geek extraordinaire, applying for the "perfect job"--felt when I realized, two seconds after hitting "send" that the subject line in my email read "Attorney Advison position" instead of ADVISOR.
I decided that correcting it would only call attention to it, so I figured if I'd shot myself in the foot, I'd live with it.
After I was hired, I talked to my boss and a number of my colleagues (it's a VERY collaborative hiring process here--EVERYONE reads EVERY application and all are involved in the interviewing), and not one single person noticed my glaring typo.
Thanks, Universe!