In the days prior to computers and designers setting copy, the typesetter was a buffer in avoiding typesetting errors. Typesetting companies had internal proofing processes in addition to the proofing stages that exist internally in an agency or studio. Copy would be proofed multiple times before going to print. Today, that typesetter buffer to protect a designer and/or agency from typos no longer exists. So, it is very important for you and the organization you work for to proof all copy carefully. You should proof everything multiple times. Be paranoid to the extreme. Typos cost you or your employer money and loss of reputation. Make sure when the final art is being approved by the client, that they understand they also have a responsibility in making sure there are no errors in the copy.
Tips on proofing copy
1. Find a quiet place and time to proof. Don't proof with someone hovering, waiting for you to get done.
2. Read the copy slowly and carefully.
3. Read the copy backwards from the end of the copy to the beginning. This forces you to break down the copy word by word.
4. Get other people to proof the copy. They will see things you will miss, since you are too familiar with the project.
5. Create a sign-off process of all those responsible for the accuracy of the project. Get signatures! Cover your butt.