Everyone who enters Paradise deserves to be there, out of the wisdom and decision of Allah. Paradise is a pure place and there is no evil in it. The dwellers of Paradise are recipients of God's Mercy. He has forgiven their sins and allowed their entry. There will be those who have to do "time" in the Fire for sins they did in this life before they are forgiven and allowed to enter Paradise.
Justice in Islam is to place something in its proper place. The greatest justice is to properly acknowledge one's Creator and to worship Him alone. The greatest injustice is to deny and reject Him and to divert worship, which is His exclusive right, to other than He Who created you. Whatever Allah (God) commands is just, and He forbids from all forms of injustice.
Morality is defined by Islam. Whatever Allah commands is what is for the best for humanity, and whatever He forbids is that which would corrupt humanity. So immorality is not something that is ignored in Islam. Rather Islam defines immorality also.
As for the question about perfect or imperfect people, then I'm not sure how to answer it because I've never heard of a perfect person or a person with no faults, flaws or mistakes and I'm not sure they exist.