Interestingly, it's possible to be both imperfect and perfect at once, if you go by general Christian theology.
Most Christians consider humans to be by definition imperfect, this being a result of the Fall. Jesus is also generally considered to be a perfect human being. Therefore, even the most perfect human being is still by definition imperfect in some measure, simply by virtue of being human.
Considering the mischief Jesus got himself into as a child, (check Luke 2:41-52) this seems to work out fairly well.