The challenge of healing should come from deciding who to heal, deciding which heal to use, and managing one's resources all while remaining cognizant of the environment. The actual process of converting the desire to cast a heal to that heal actually going off should be as seamless as possible; for many people mouse over macros and click to cast go a long ways towards accomplishing that. Furthermore, the UI should present relevant information, such as the status of HOTs and shields, in a easy to read, non distracting, and customizable fashion. Dealing with the interface should never be the hard part of an encounter, and I think the default UI still has a ways to go to accomplish that. The fact that healers can contribute non-negligible DPS in this game further enhances the need to streamline the interface so that the player has time to engage in tasks other than healing.
As an example of areas requiring improvement, I've been leveling a combat medic commando as an alt and found the targeting system to be lacking when it comes to using hammer shot. Let's say you want to cast two heals on yourself, separated by a hammer shot in order to stay in the highest regen range. This requires you to target yourself and cast the heal, target something else and cast hammer shot, and then retarget yourself again. This just seems unnecessarily clunky.