Holy Priest is a lot different from Holy Paladin. The first major change is that there are a lot more buttons. As well, most of the heals are targeted. Unlike my paladin, I found it was easier to heal by just targeting friendlies.
I find the "Word" mechanic hard to get used to. I need to get better at using those spells on cooldown. Instead of treating them as part of the rotation, I treated them as cooldowns, and didn't cast them nearly as much as I should have. WoWAnalyzer scolded me for this.
I think I've mentioned this before, but I find spells with cooldowns in the 30 to 90 second range harder to keep in mind. It's short enough that you should use them on cooldown, but long enough that they fall out of memory and are easy to forget about.
One thing, though. I thought Holy Priest was a mana-thirsty spec, but it didn't seem like it to me. I even cast a lot of Flash Heal, which is more than I should have. Maybe I'm not casting enough, or perhaps I'm supposed to be spamming the AoE heal. I did check WoWHead's Holy Priest guide beforehand, and I was trying to follow that.
Maybe I'll see if I can take the Priest to the first three bosses of Nyalotha Heroic this week, and see how healing is in the harder environment.