What's the best way to tell your boss, who is ...

I actually don't think you need to say anything to your boss. What you need to realize is that you're getting paid to do a job to the best of your ability. If you're doing your best, and not allowing other things distract you while you work (like music or other background noise), there's nothing to say to your boss.

I suggest you ask for another checkup. It will seem extra responsible on your part, and it seems reasonable that someone who is very familiar with a certain text will not notice all the problems.

I think you should quit your job and find some work that you are qualified to do. If your boss is not happy with your lousey performance than you should quit before he fires you.