When you see the same copy again and again through the different stages of production, you will miss new errors. Fresh eyes are needed. If it's as plain as the nose on your face, everybody can see it but you. These are precisely the places proofreaders are most likely to miss. Mistakery loves company.
Errors often cluster.
When you find one, look hard for others nearby. When you change horses in midstream, you can get wet. It's easy to overlook an error set in type that is different from the typeface you are reading. Watch out when type changes to all caps, italics, bold face, small sizes and large sizes. Watch out when underlines appear in typed copy.