A Christian will always say that injustices by God cannot exist. God is just and therefore everything he does is just. The fact that imperfect humans don't agree with Yahweh has nothing to do with it. I generally try to avoid biting on the "name some injustices carried out by God" question because it's not a winnable argument. Not only can God choose to do what he wants to and still be just, but he can also be wishy-washy. He is God. It is his right to do so. How can we as mere humans (and sinful ones at that) question him?
At the same time, though, God--assuming he exists--can't seriously expect all humans to just accept at face value everything that is in the Bible or any other religious text. The brains that he gave us are going to demand that we question things that do not make sense. And I don't care what Jewish or Hebrew religion you belong to, it is undeniable that from a human standpoint, there are many things in the Bible that do not make sense.
Why did the Yahweh deity never hesitate to show who was boss, often cruelly striking down thousands? As mentioned in another of my topics, once he cause 42 children to be mauled because they badmouthed on of his priests. Yet Jesus always scolded his apostles whenever they reacted in a way that suggested that enemies of Christ should be dealt with.
This is why the Bible seems contrived and outdated. Three thousand years ago it was acceptable to kill people for what we might call minor offenses, regardless of the deity worshipped. In some places that we would call backwards or undeveloped now, some of these beatings and killings continue and the communities feel they are justified.