Love certainly does not mean ignoring sins or not noticing them at all. It is unloving for us to notice a fellow Christian living in sin and not help them. And when they sin against us, we are not to act like nothing happened in all cases, but we are to confront them Biblically when appropriate.
R.C. Sproul Jr. wrote an excellent article on the subject here. In summary, he said:
When we are wronged our calling is to practice a careful moral calculus. Is this offense one I should let go of? Is it among the multitude that love covers? Or is this offense grievous enough that love means confronting in grace my brother? Sadly what we usually do is think we are practicing the former while actually holding grudges and putting miracle-grow on roots of bitterness. Peace in the church calls us to under-accuse, over-repent and over-forgive. Let us not be afraid to call sin sin, but let us not be slow to forgive it and to look past it.
There are cases where we are to overlook. If they were inconsiderate and bothered us, in many cases it is better to simply overlook and move on. But if the sin is greater, then we should confront them using the model presented in Matthew 18:15-19. In all cases, we should have an attitude of forgiveness towards them, willing to forgive the wrong when they ask for forgiveness.
In relationship to God's love towards man (and you could probably ask a second question on this part), we are to love because God first loved us. He paid the price for our sins on the cross, and forgave us our sins:
For as high as the heavens are above the earth, So great is His lovingkindness toward those who fear Him. As far as the east is from the west, So far has He removed our transgressions from us. (Psalm 103:11-12)
God's justice demands there must be a payment for our sins. But because Christ died on the cross for them, God forgives us if we truly repent. Sometimes, God confronts us with our sins using some earthly method. But God always forgives, and we should too.