Both the shields are highly useful for downstairs healing (like solo healing downstairs Heroic 10m, where as when we used a paladin, one of the tanks would always die prematurely, usually to the worm spawn all hitting 1 tank at same time... instagibbing them).
As for the Guardian spirit, having more than 1 of these in a raid is completely useless. Guardian can only be used on the boss like once every 40-50 seconds, making chaining 2 Guardians impossible. The glyph on the single priest, is enough to pretty much use it on almost every downstairs phase, while a PI, on a Pally/sham, with a guardian spirit up = big green numbers (usable every other downstairs phase, throughout the fight, and is chainable for even more of those 'big green numbers', 2 Disc priest's were used to chain PI's on several of the top HPS parses for Dreamwalker).

As for the general focus of this guide, I'm more or less just pointing out, that both spec's of the Priest, are viable raid healers. More to the point, both spec's are actually much better at raid healing, than they are tank healing.

Here's one of my favorite log parses now, Resto Druid + Disc Priest healing comp for LK10HM! (Resto druid tank healing)
WoW Meters Online - Combatlog Replay

So judging by what I seen, how viable are renew priests in ICC25/10ICCHM and so forth?

I used to renew all the time but then I swapped back to spamming PoH and throwing PoM and CoH whenever they were up in heavy raid dmg fights, BQL, etc.

Could I just focus on renewing two groups and CoHing clusters of people while throwing PoM and the occasional flash heal to keep serendipity up?

HoT's are viable for Holy, to an extent.
I don't care for renew, for a simple reason, its a HoT. Glyph of Rejuv was the worse possible glyph they could have ever invented, it illustrated the hole in resto druid healingl. That glyph, when used, was healing for 2-4% of their total effective healing, which proc'd when they healed someone under 50% hp, and healing for +50%. So, of all the meter padding the druids were doing, they actually were only healing the people that NEEDED to be healed, 4-8% of the time (since glyph was 1/2 the amount they were healing during this time).
Personally I see that as unacceptable (for a priest at least), as thats usually what leads to premature death's. Sure a Flash Heal talent spec, may look slightly lower on the pure meter side, but you'll be spending a lot more time actually healing people that are in danger of dying, instead of sniping that 1k health deficit on 3 other players at 98% HP.

But thats my opinion for Holy at least (Disc though = Bubble Bot w/ Penance spot raid healing as needed)

I was doing the math of a disc priest's mana regeneration for a friend of mine last night and came across an interesting conclusion that I would like to confirm. No, I am not a priest but I am asking for confirmation of my calculations about priests.

Given the Mana Regeneration Formula shown for 3.1, the value of spirit for a disc priest as a regeneration stat seems diminished due to lack of regeneration OO5SR.

5 x 0.00575 x 0.6 x SQRT(Intellect) x Spirit = OO5SR Mana Regeneration

To get I5SR Regen with Meditation, Multiply OO5SR Mana Regeneration by 0.5.

Assume with MOTW, Arcane Int, and Kings a Disc priest has 2000 Intellect. Solving for the end value of spirit as OO5SR Regen (X), I used the following equation:

5 x 0.00575 x 0.6 x 44.721 = 1.06X

X= 0.8177 (Rounded to the fourth decimal place)

This results in an I5SR Mana Regeneration Value for spirit of 0.4088. Kings increases this value by a factor of 1.1, raising it to 0.4497.

This means that it requires 2.2237 Spirit to amount to 1mp5.

That said, assuming access to all BIS gear, would it be better to use Sp/Mp5 or Haste/Mp5 gems for blue sockets that are being matched to achieve socket bonuses as opposed to SP/Spirit?

It's actually 0.005575, not 0.00575, if our historical formula is correct.

The end result for discipline is 0,4361 MP5 per 1 Spi @2000 int raid buffed.

Neither.
Disc Priest's main source of their blue energy bar, is Rapture proc's. Its a proc that happens when PW:S is completely used up on our target, the priest gains 2.5% of his max mana back but 'on a 12 sec CD'. This effect, has a flaw though, given game lag, any shields broken from the same instant dmg source, all proc Rapture at the same time (because the game can't distinquish between them). This results in 3-8 PW:S's all proc'ing rapture at once = small innervate (7.5-20% of 37k? mana pool = a lot... everytime LK25 HM does an infest, I go from xx% mana to 100% everytime :P).
As for gemming, a Disc Priest should be basically stacking all spellpower (probably well over the haste cap. crit only has a large impact on Aegis bubbles, leaving just Spellpower). This can cause some issues on fights, where the number of rapture proc's are limited to 1-2 per ICD, in these scenarios (IMO) its best to use endurance trinkets, since they are easier to switch out.

"because the game can't distinquish between them" isn't quite true. Blizzard does have code to identify multiple rapture procs and subsequently only let one of them pass. This code is active in Ulduar, at General Vezax (can be easily verified in P2, hard mode). There, you will get one proc with reduced effect, but only one.

To me, this is proof enough that the mechanics of multiple rapture procs is fully intended by Blizzard and can be disabled in every fight where the game designers wish to do so.

This was a typo on my part. Not enough 5s. However, the calculation I used is the one given on page one of this thread.

This equation assumes the value of spirit to be 1.06X, which is to account for Enlightenment- a 6% increase to spirit. However, I am unsure whether it scales before or after Kings. The equation assumes that it is before. If it is after, the value of spirit becomes 1.166X, which dramatically changes the results to those of Hegen's calculation.

The disc priest in question is horde side, therefore the Human component of the equation was excluded.

I concede that they are close, but assuming that all elements of the equation are correct, MP5 from the gems mathematically equates to a higher regeneration gain.

(1 x 1.06) x 1.1 = (1 x 1.1) x 1.06 = 1.166

It doesn't really matter which way you multiply that, its the same equation.
But, the math has already been worked out, ages ago. Thats one of the first things thats reevaluated each time theres a major change to regen formulas, but, they always had the per spec modifiers that needed to be calculated into each.
Changes:
Broke down Holy+Disc conversions, Holy gained 10% kings bonus and 5% spirit bonus to those appropriate stats, Disc received 10% kings, 15% int, 6% Spirit (per talents).
(people are welcome to check my math, it is getting kinda late here :P)

But yes, back to your point, from a gem aspect, 10 spirit = 3.65MP5 vs 5 MP5 from gemming Purified vs Royal, yes, is a higher net yeild of MP5. But, intellect is nearly double the value of spirit for a Disc priest. The total being 0.7089 MP5 per point of Int (vs .365 for spirit).
But again, we're going back to the underlying cause, a Disc priest in ICC gear, shouldn't require higher regen, due to the heavily broken mechanic of Rapture shield proc's (Rapture = 364mp5 per shield every 12, multiple shields that pop when this is not on CD at the same time, all yeild the proc, so thats 364mp5 x1-x20....).
Also, using a regen flask vs spellpower flask is also an option, but the numbers still support Flask of Distilled Wisdom, as the higher source of MP5 (Distilled wisdom =46.07 mp5 vs Mojo = 45 mp5).

Sorry to say this, but some of the numbers in the current guide are actually incorrect (not the basic formulas nor the reasoning). I have an update in preparation, that lists both the values for disc and holy, with and without talent/buff gains. Still need to redo the HC stuff, though, assumptions no longer really match healing styles close enough.

Bugs (obvious issue with int/spi baseline aside):
- Replenishment value is pre-nerf.
- mp5 gain from int on meditation is too high (seems to already factor in talent/buff gains)

Regarding your numbers: I will compare these with my spreadsheet before posting, that's a welcome input (and well timed, too).

Regarding rapture: this behaviour already was insane at, for example, Freya+3, though it was more difficult to pull it off reliably there. The thing is, it's undeniable that at General Vezax they disabled the multiple Rapture procs without turning off the Rapture on self entirely (I think it was reduced to about 30% or so). So, while what you say has merit, this clearly proves to me they are a) aware of this since a long time ago and b) are able to disable this if and where they wish do to so.

My real question about the above is where you say stack haste up to 12-14%, but then say the goal to start Icecrown for haste is 30%. I think there must be some error here, or perhaps I simply do not understand.

At my peak in ICC I had about 24% haste (I am a holy priest), and was focused on raid healing using PoM, CoH, FH and PoH, stacking via serendipity in order to power faster PoHs. My personal experience has seemed to be that due to the nerfing of the coefficient for PoH in Ulduar, and the negative impact of scaling since then, that PoH is beginning to move into the realm of GH as a no longer in actual use good spell. PoM in 4 piece tier 10 seems to be almost as good as CoH in terms of ehps.

With all the druid HoTs, quick pally heals and CH spam, what appears to be a productive and effective spell (PoH) too often ends up with too little effective healing and too much overhealing by the time it connects. There is also the complication of people in groups being scattered on many encounters.

I have recently started experimenting with moving away from use of haste, serendipity and PoH to greater use of SP and Renew spam. I still value haste, but I have in experimenting started regemming so as to replace haste with more SP.

I will be interested in any experience others have with such a modified playstyle in ICC as a holy priest.