I came across this fabulous wand that instilled Heal III ability -- only, I still healed with Heal I -- is there something I'm doing wrong, or is this a glitch/bug?

You might have found the solution already or not remember details, but:
Did you "equip" the Heal III? In the "Skill" window the boxes at the bottom. (Default are "Attack", "Block" and "Excape" and 2 empty slots, but you can change every single one of them to whatever you want.)

Yep you have to set the ability in your skills list.