Note that this has been edited to reflect the changes in Cataclysm / The Shattering, so the stat weighing is not final and a proper raid-balance of stats is not concrete.
Int provides you with spellpower and a larger mana pool, so it is naturally a strong stat.
Haste is also important, as it allows you to cast your spells faster, and to an extent, reduces the GCD (which makes a difference for instant cast spells). You get a good amount of haste passively through talents though (9% through Judgements of the Pure, 3% through Blazing Light, plus flat cast reductions on certain spells).
Crit is always nice to have, and it synnergizes nicely with some talents (Crit Holy Shocks reduce cast time on HL / DL, for example).
Mastery (at 80 and beyond) gives your heals a bonus shield equal to a % of the heal amount on your target. Shield effects have always been quite effective, and this more or less gives you a permanent Valan'yr effect to work with. I can see this being a very popular mastery, however we'll have to see how well it scales further on.
Spirit is now the go-to stat for mana regen as of The Shattering, and will continue to be so throughout Cataclysm. There may be a FEW items / enchants out there that provide MP5, but for the most part you're looking for spirit for your regen needs. It still remains to be seen just how much spirit is going to be needed to sustain throughout hardmode fights (especially with the ability to Judge Seal of Insight AND Divine Plea as decent mana regen abilities), but regardless, Spirit is the new regen stat.
As for leveling, just worry about Int, Crit, and to a lesser degree, Haste. Early on and leveling, a lot of healing will be done with Holy Shock and Word of Glory, which are both instant. Haste wont play a big role until later when you need to utilize your Flash of Light/Holy Light/Divine Light spells a bit more.
Best Answer
The distinction is in if the healing effect is a 'tick' or directly attributable to the spell. Whenever someone is healed, ask this question:
Does the spell that caused the heal to happen cast in the same frame/game logic tick as the heal itself?
Iff yes, then this is a direct heal.
Iff no, and there are multiple instances of time in which heals happen, it is periodic. This includes both DoT and channelled effects.
Counts as periodic
Not actually periodic
1: Only the initial cast will remove a Grievous stack, not every tick.
Interesting cases
For some spells/effects, it's unclear of whether they would count, and likely up to the developer. As it's unlikely every corner case was covered, there may be some surprising inconsistent details. Consider effects like:
It's likely up to the specific code implementation of each spell whether or not Grievous would count them as periodic or not. Someone would have to make a giant list of spells and test each one if they count.
It's quite likely most of these would not count as periodic with a few exceptions.