How well do you pay attention to detail?

Writing it all down in a safe and reliable place. You never know what details are important. In fact, the details that you don't think are important are the ones you are going to forget!

Keep a work or life journal in a spiral or some kind of bound notebook. Make it a small enough size that you can carry it with you everywhere. Take notes, write down phone numbers, and create 'to do' lists in its pages. You will find yourself reading through the last couple pages every so often to make sure you have gotten everything done or going back a couple weeks to find that phone number/email you wrote down. It is also proven if you write something down you are more likely to remember it.

Also writing down instructions from a boss helps you visualize project/assignment and hopefully come up with some proactive questions to clarify the assignment (and thus be more detailed). Likewise, writing instructions/deliverables down and reading them to your boss help confirm that both of you are on the same page.
Even if "pay attention to detail" refers to not making mistakes, creating checklists in your work/life journal can help you to remember to go over places where you normally make mistakes. For instance, if you normally send out poorly spelled emails, referencing a checklist can help remind you to take the time to read the email out loud before you send it or be sure to run the spell check.

It isn't always about paying attention to details. Sometimes it is about admitting your weaknesses and/or mistakes and figuring out ways to work around them. Everyone forgets the details. You just need to record them in some kind of systematic way so that you can review and remember them as you go along.