Aside from the craziness of naming a skill "skill", i.e. Weapon Skill Skill and Ballistic Skill Skill, it seems like there was an obvious oversight in listing Specializations when the equipment section lists different Categories that are not listed in the Specializations. Of course, the list of possible Specializations is not meant to be exhaustive, but when you go to the trouble of creating categories of weapons, why not list those?
From my read, the following should be specializations available for Weapons and Ballistic skills:
Weapon Skill (St): Cavalry, Flail, Fencing, Ordinary, Great Weapons, Polearms, Parry, Spear, Unarmed
Ballistic Skill (Ag): Bow, Crossbow, Thrown Weapons, Blackpowder Weapons, Sling, Entangling
Also, I changed Hand weapons to Ordinary as that's the actual category, and reduced Parry to simple Parry instead of splitting it between hand weapons and great weapons. Given the wide range of types to specialize with, if you were to break Parry down by type, you would have to have all the different categories (Parry with Spear, Parry with Polearms, etc.).
I hope this could be included with errata as it really doesn't make sense to have weapon Categories and then ignore those categories in the skill specializations. Also, finding a different name from Weapon Skill and Ballistic Skill would be less redundant.