Perfectly Perfect is about being in love with someone and seeing beauty in every part of them, even the parts they don't like about themselves. People tend to focus too much on their flaws. When we see a picture of ourselves we tend to comment on the things we hate, when in reality nobody really notices, especially when you love the person. All the little "flaws" become things that make you special and different.
Most of us in the band are now married or in long term relationships and this song was definitely inspired by that. For me personally, the song really reminds me of my wife.