You are going to need a kick-ass cover letter! Don’t be afraid to let them know that you are excited about the possibility of working for them. And always take the opportunity to tell them that you think you would be a good fit for the position.
Your objective. Make it about the benefits hiring you will bring. Maybe something like: To work with a team of exceptional creatives. In a fast paced challenging environment where I can use my design skills to grow with the productivity and reputation of the company.
The bottom line is that freelancers eat their mistakes. Even though my client signed off on the piece, I would have ended up paying to re-print it. I got off lucky with just paying for the correction and new proof.