The attributes of God are all good--on this we can agree. But there is something about God's attributes that may surprise you: they can be in tension--and this prevents some from being "omni" attributes. For example, God is just and God is merciful. But those attributes are in conflict—mercy is not a subset of justice. In fact it is orthogonal--as we'll discuss later.
When discussing God's attributes it is worth reminding ourselves what we all know: there is only one attribute of God that is described in the Hebrew superlative: God is holy, holy, holy. No other attribute is described in that manner. Nowhere is God described as just, just, just, or love, love, love.
Aside: what does holy mean? I don't know. Not really. I can catch glimpses of it—especially when Isaiah has his vision (Woe is me—I am unraveled!) Whatever it is, it is the defining attribute of God, the trump card. I am persuaded that our ability to understand God is severely limited by our inability to comprehend holiness.
So in terms of the "omnis" we can at least be certain that God is omniholy. We can further deduce that God is omnipotent—but only if we understand what that means: it means whatever is possible, God can do it. It really means the same thing as saying: God is sovereign. It does not mean that God can do the impossible. If God, as it appears, has created a universe that has no center, then God cannot put us in the center of the universe. Because, well, it has no center. God, in short, cannot violate the law of non-contradiction. Likewise we can, I believe, infer from scripture that God is omniscient and omnipresent. (Another aside: If you think hell is the total absence of God—I say you are wrong. His presence--If I make my bed in Sheol, you are there--may well be a large component of the agony of hell—but I speculate.)
Instead of the prefix omni, some like to use the qualifier infinitely. That is more nebulous—but fine—we can agree that God is infinitely holy, infinitely knowledgeable, etc.
Trouble arises when people insist that God is infinitely X, when the bible clearly indicates that God is most definitely not infinitely X.
A common tactic is to claim that God is omnibenevolent, a presupposition that more than a few Christians would mistakenly accept, and then to display, trivially, that God is in many cases not benevolent—ergo, game over man, no God. We should never fall for this cheap trick. The bible is explicit: God is not benevolent, benevolent, benevolent. Just ask the "ites" who stood in the way of the Jewish conquest of Canaan. Or ask Esau. Instead of infinitely benevolent, God is particularly benevolent. He has mercy not on all, but on those it pleases him to have mercy, such as Jacob. He works in all things for good (in that sense he is all-good, or omnigood, or infinitely good) but he does so only for the benefit of a subset of all people: those who love him (in that sense he is not infinitely benevolent.)
Benevolence is, in fact, in tension with omnipotence of sovereignty. A God that must be benevolent, in all circumstances to all creatures, is a God whose sovereignty is severely restricted, a God who is obligated to behave in a certain manner.
Back to the example of God's justice. God is not just, just, just. Which as we know is a good thing. In our own country there is a movement to make our own judges just, just, just by enforcing mandatory, uniform sentences—with predictably, at times, disastrous results. God's justice is at tension with his mercy--and thankfully he chooses not to be, or rather his nature is not, infinitely just. In a diagram it looks something like this:
God's mercy is at the expense of his justice. He sacrifices being infinitely just in order to be merciful to some. Justice implies uniform sentencing for the same crime—but God has mercy on some. The negative side of non-justice—injustice, is not found in God. Nobody receives a punishment they don't deserve.