The biggest way that I improve as a healer is by learning the fights. Really paying attention and trying to understand each fight is key.
If you can predict when your raid is going to take damage, your reaction times will improve, and you will be able to choose the most effective response for that damage.
Other than that I try to improve my macros and power aura alerts.
This. Just do the fights until you can do them blindfolded. Know your spells, know your abilities, know the encounter and know how good or doofus your team mates are. Improvements such as mouse-over healing, macros, specilised addons...well, I personally don't use them and never will. Point click ftw!