Before the 1.33/1.34 patch, the weapon expertise skills with a fixed damage bonus range were broke (any speed bonus, etc. was applied, but not the damage), as was True Shot.
With the 1.33/1.34 patch, the weapon expertise skills were fixed, but True Shot was not.
Some (most/all?) of the skill bonus damage is not be displayed in the character stats pane since it may be randomly applied, and when applied it may be partially or completely resisted.
Axe Expertise works fine, though after the catacombs there are more (and more powerful) swords consistently in the game.
