No pain, fear of death, or honor.
Just about any opponent who truly does not fear pain or death is one not to be taken lightly. Consider honey bees, cornered animals, or battle androids (I'm sure we're all familiar). These skeletons will throw themselves onto a blade or in front of a spell to allow their comrades slightly more time to advance on their target. They'd throw bone dust in the hero's face with a dagger to the eyes close behind. They'd fight dirty and to the death. That's not something anyone will have an easy time dealing with.
The bigger problem is, how do you actually defeat them?
A human skeleton has over 240 degrees of freedom. That's a lot for a mage to control all at once. But can clearly be accomplished by a human mind (we're doing it now). The skeleton is controlled by magic, the only reason to use a human skeleton is so the natural reflexes of the mage apply to the same kinematics of the controlled specimen. The controlled skeletons don't care about broken bones, but having an arm that now bends in five places is a bit harder for the mage to control. The mage could give up control over a broken limb for a gain in control but a loss in fighting ability. But no mage is strong enough to make a functioning warrior out of bone dust. Smash them to dust and the hero wins. Blunt weapons are the way to go.