These are the major things that I believe would put priests up there with all the other healing classes.
Spell Protection - Priest healing spells aren't very strong. We aren't known for a monstrous heals, most of our healing comes from shields. Divine Aegis/Power Word: Shield/Pain Suppression are one of the biggest healing spells priests have. I consider them healing spells instead of absorb spells because it allows for healing because the target isn't taking any damage during that period. Priest healing all revolved around our ability to shield allies from taking damage while healing them, but after the dispel changes almost any class can take off these absorbs with ease.
My fix: Bring dispel protection back, 3 points, 20/40/60% chance for your spells to not be dispelled.
Mana Issues - Another major problem priests experience is the huge amounts of mana required for our spells and while we have spells such as Shadowfiend/Hymn of Hope, outside of these spells we are basically destined to experience problems running out of mana. Archangel was a step towards the right direction, but I'll never be able to successfully cast 5 smites, and even with 5 smites at 2.5 second cast each the benefit is still too small.
My fix: Make smite a 1.3 second cast equivalent to paladins exorcism, reduce smites mana cost by 50%. Allow archangel to refund 15% mana on a 20-30 second cooldown.
Power Word: Barrier - This spell was decent before the 30% reduced damage change, but after that it's mainly good for PvE rendering it basically useless for PvP. The area is too small and in an arena situation the fight shifts drastically almost each second across the map.
My fix: Revert the Power Word: barrier change to its previous self. Allow it to put a shield on everyone in the party/raid absorbing a certain amount of damage. In a tough situation, plenty of raid members/arena partners will be taking damage at the same time, using this will allow the priest to catch up on healing and temporarily stopping the income of damage.
These suggestions were formulated based on solely my opinion, feel free to add/remove from it.
All I've been seeing lately are whine threads with no one really addressing the issues that need to be solved, therefore this was the proposal I came up with.