Open Question: Will an employer background check review my date mistake?

I just applied for a position. The people called me back about my resume stating they were very interested in me for potential employment. However, I noticed a mistake on my resume. For my current employment, I started in July of 2004 and I must not have been thinking correctly or made a typo or something because on my resume it states 2003. I didn't deliberately lie about it, but I was too afraid to correct the woman when she said "Wow! So you've been there since 2003!" I didn't want them to think I made frequent mistakes on my typing or anything. I'm paranoid because I really want this position, but I'm afraid a background check of my employment history will reveal the mistake and they might take it for a lie and not hire me. Will a background check reveal this date or will it just confirm that I did, in fact, work there?