Mohler is known for melding Romanticism, German Idealism, and old-school Baroque Catholicism into a theology. Nonetheless, he didn't write a system. He mainly wrote on the doctrine of the Church itself. His most famous work was called Symbolik or Symbolism (auf English), where he compared the Lutheran and Reformed confessional writing with those of the Catholic Church.
His theory is that Protestants in general are wrong mainly because they don't understand the state of Adam and Eve before the Fall. Now, that's an interesting angle! Nevertheless, before we explore his interpretation, I need to do some explaining as to how Catholics think about these things (particularly for a mostly Lutheran audience).
Catholics distinguish between what they refer to as "Grace" and "Nature." Nature is the givenness of creation. It's what a creature just is on its own without any divine help or intervention. In a sense, God sort of owes the creature to be what it is. God is a designing subject and he makes a world that will be like himself so that he can desire it along with himself. He gives the world a certain integrity in its desirability that he wouldn't eliminate or transverse. In fact, he really ultimately can't, because it's just not what he wants to do.
Then there's "Grace." Grace is not exactly divine favor like it is in the NT (though it certainly involves favor), but rather it's a capacity which God alone bestows that helps creatures transcend their own nature. God made nature to be "ordered" towards grace. For example, he made human being with certain divinely infused attributes that would help them to relate to God. Now, although it is the goal of human beings to relate to God, it isn't owed to them to do so and it's not naturally part of their capacity.
This gets us back to Adam and Eve. Adam and Eve, according to Catholicism, didn't naturally have the capacity to relate to God. Rather, God gave it to them as a grace, that is, he gave them a bunch of supernaturally infused qualities. Eventually they would have earned enough merit by using them in order to ascend into heaven and be with him, participating in his act of self-enjoyment and knowledge.
Why do they suggest this about Adam and Eve's natural capacities? Because according to their thinking if Adam and Eve had naturally been able to relate to God, then the Fall would have actually damaged their nature. If that's the case, then God would be unjust for having taken something away from them, something that he owed to them, that is, the integrity of their nature. Instead, he took away from them after the Fall what he never really had to give in the first place, grace. Secondly, if human being naturally would have been able to merit their beatification, then they would naturally been able to make a claim on God regarding salvation. In other words, if you believe that free will + merit+ grace= salvation, then getting ride of the grace part will take away your fail safe mechanism that is supposed to guard divine sovereignty and militate against Pelagianism.
The Reformers all rejected this way of thinking. They claimed that human beings prior to the Fall had naturally been able to relate to God. Consequently, the Fall really had damaged human nature and humans were radically dependent on God for their existence. God, at the end of the day, didn't owe human being anything- even the integrity of their nature.
So, Mohler claims, this shows why Protestantism is messed up. It means that human beings can never be touched by the grace of God as he understands it. They either don't need it (before the Fall) or they are imputed with Christ's righteousness, and therefore don't need it in the era of redemption (Mohler apparently doesn't get the distinction between justificaiton and sanctification, but I've known many Catholics who don't understand Reformation teaching on this point). This ultimately means that human beings will never be able to transcend themselves. They will always be stuck with their own finitude and justification will become a sort of "external mechanism" as he puts it.
I've read some this before in Henri De Lubac's book Augustunianism in Modern Thought. De Lubac takes it a step further and suggests that if human being could actually naturally relate to God prior to the Fall, then it would mean that they could naturally control God by their merit. Grace means that God allows them to make a claim on him by meritorious behavior, but at the end of the day, it's all dependent on God.
The amusing thing about all this is that none of these guys get that their critiques only work if you assume the premises of Catholic thought: 1. Humans can merit things. I.e. they can lay some sort of claim on God. 2. Nature itself is a given- that is, that much is owed to us, etc.
Read Luther's Small and Large Catechisms. Everything is grace- that is, grace defined as divine favor. Creation isn't something that God had to do (though I don't think that De Lubac or Mohler want to say that exactly), it's a perpetual gift. God doesn't have to continue sustain creation. Everything is a perpetual gift. The natural response to God, Luther tells us, is the receptivity and gratitude of faith. This is true of our faith in God the creator and God the redeemer. Faith in Christ actually continuously receives a new creation in Word and sacrament.
So, with Luther, the whole distinction of grace and nature breaks down. Everything is grace, both new creation and old creation. Our sin is that in our unbelief we are unreceptive to it.