Most of the contradictions we perceive stem from a misunderstanding of the depths of the riches of God's goodness and his judgement along with a commensurate misunderstanding of our own fallenness. It is always dangerous for us to use ourselves and what good we think we are capable of as the standard against which we evaluate God. Paul Chernoch has given a good answer in regards to the love and mercy of God.
"For while we were still weak, at the right time Christ died for the ungodly. For one will scarcely die for a righteous person—though perhaps for a good person one would dare even to die— but God shows his love for us in that while we were still sinners, Christ died for us." - Romans 5:6-8
It is also good for us, in light of God's mercy, to deepen our understanding of our own sinfulness for it is "while we were still sinners" that God loved us through Christ. God's Grace is magnified by how far down it has reached to redeem us. Not that we should rejoice in our sin or sin more to highlight grace but that, recognizing the uncrossable chasm that exists between Righteous God and wicked mankind, we might repent and call on the name of the Lord for mercy and grace.
Some of the things Jesus said about our fallen condition are painfully illustrative:
"If you then, who are evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him!" - Matthew 7:11
"There were some present at that very time who told him about the Galileans whose blood Pilate had mingled with their sacrifices. And he answered them, “Do you think that these Galileans were worse sinners than all the other Galileans, because they suffered in this way? No, I tell you; but unless you repent, you will all likewise perish." - Luke 13:1-3
"Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. Do not marvel that I said to you, ‘You must be born again.’" - John 3:5-7
God judges us according to the thoughts and intentions of our hearts and we are not qualified to accurately read what is going on at that level even in ourselves. Even the apostle Paul, though he lived very carefully and was unaware of any wrongdoing in himself, did not claim to be justified by his perceived innocence but acknowledged that the Lord is the judge.
Finally, look to Job who, in the midst of what he (and perhaps we all) perceived as unfair treatment, longed to put God in the dock and cross-examine him. When God showed up, Job was undone and God's merciful rescue of him began when Job prayed for the "friends" who had been tormenting him.