Rapture is phenomenal but probably bugged. Be prepared to go back to Holy.

Spec
As a raiding Shadow Priest, my preferred spec+glyphs is http://www.wowhead.com/?talent#bVcbuZZGxfVRfzcfqszAo:hqazc0
The basic Shadow spec is as I linked it, but the 1 point I put into Imp. SF can be put basically anywhere you want. I prefer Imp. SF so that I will always get 2 tics on mind flay (which is useful for grinding and on certain encounters) even if I'm taking some spell pushback.

Casting
As SW:P is still not updating based on your current stack of Shadow Weaving, it is best to cast SW:P after you have a 5x stack of SW up. My advice for your initial cast sequence on a boss is this:

1) VE (optional)
2) VT
3) MB
4) MF (let it tic 3 times)
5) DP
6) SW:P

The reason I cast VT+MB as my first 2 offensive spells is so I can get Replenishment tic'ing asap. After that, I cast Mind Flay for a full duration as each tic currently applies 1 stack of SW. After the Mind Flay, I'll have 5x SW and will then cast DP (as with its buffs in 3.1 the extra 10% dmg is nice) and then SW:P, though SW:P and DP can best cast in opposite order, it just makes more sense to me to have DP's cooldown up sooner rather than later.

Shadowfiend
As our Shadowfiend now does more damage and has an ability that is good to use, I'd recommend at least using this macro which you can spam while you cast your other spells for the duration of your Shadowfiend's life.

#showtooltip
/cast [nopet]Shadowfiend
/cast [pet]Shadowcrawl

Or, if you don't want to even think about it, you can just put

/cast [pet]Shadowcrawl

in a macro with all of your abilities, so whenever your Shadowfiend is up it'll automatically cast Shadowcrawl without you having to think about it.

Mana Regen
The new glyph, Glyph of Dispersion, is unrequired as a raiding shadow priest. The only time this may not be true is if you're a new 80 and have mana issues, in which case this glyph will help a lot. For the rest of us, 3min Dispersion and 3min Shadowfiend are plenty of mana regen to keep us going (if used properly) throughout any fight.

Preformatted Text is fun!

We lost a lot of mana regen, but the shadow fiend makes up for it, use accordingly.

Ulduar is hard, be ready for large repair bills.

Don't talk to the stone guy at the start of Ulduar, unless you want hard mode, yeah, long story.

Dual spec is your friend, work on your off set.

Glyphed and talented Prayer of Healing is awesome, if you're friends with the raid leader.

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Q u o t e:
Glyphed and talented Prayer of Healing is awesome, if you're friends with the raid leader.

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Or on fights where you're all standing in about the same place anyway (Auraiya, Mimiron p2 and XT with the way we did them.)

New Divine Hymn is a brillant OH *#%! button, especially on fights that like to have bursts of hard constant raid damage (y hulo thar XT.) Note that the spell can crit, so IFing it is a very good idea.

In Ulduar, against bosses, I have noticed that it is now more important to keep your Vampiric Embrace up at all times. Now that our dots crit, this allows for bigger VE ticks.

Cast Divine Hymn, even if you are Shadow, and especially during the tantrum on the Deconstructor. It can mean the difference between losing 4 party members, and losing none.

I noticed that you should be throwing ranged up onto the Flame Leviathan, and Shadow Priests in paticular make quite a good man for the job. Their self healing is great, and they can dot up other turrets while they are dpsing their own.

Get all the talents that help PoH and use it as much as it's needed. Try to keep serendipity up too, so you can cast 2 (currently) at a very fast speed. Excellent for raid healing as holy.

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Q u o t e:
Ulduar is hard, be ready for large repair bills.

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But don't give up!

You'll learn when to move, when not to move, when to pump out healing, when to shield, when to use cooldowns. You'll also learn how to trust your other healers and also start knowing when you need to pick it up.

As DPS, well...don't stand in the fire, stay 10 yards away from people on most fights.

Assist off the nearest Death Knight and cast Devouring Plague on their target. The DK will spread DP when they use Pestilence.

Targetted PoH is very powerful in Ulduar. It's worthwhile to spend a little time making sure the group members are in the general vicinity of each other.

Given all the "circles" raid members need to run out of, Body and Soul is ridiculously useful. This spec has proven itself to be surprisingly effective for me on a number of encounters where raid damage is either steady and overwhelming or intermittent and bursty:

http://www.wowhead.com/?talent#bVcbuhhVobZMxxcfMqqhMcz:rcV

Advice:

1) Damage meters. They are borked. Why? because who ever gets thrown into the Leviathan gets to do 1 million damage a whack. WWS is now the best thing to look at maybe, or have your meter keep the last 20 fights, so you know what dps is really going on.

2) Be prepared to heal, if you are Shadow. The hymns are not as useless as previously thought. You need to help during XT's tantrum.

3) Shadowfiend is not useless.

4) MOVE YOUR FEET. Damage meters don't mean *%@* when you are dead. Yes, it sucks losing to the rogue/DK/hunter for the damage meters, due to our need to rev up, but razorscale and XT will kick your butt if you don't move. Patchwerk is done and gone in naxx, there is no more dps the face off, you have to think.

5) AoE has not gone away. PoH is your friend.

I just wanted to give the Hymns a shout-out. Pre 3.1, they were useless and so many of us completely forgot that they were even in our spellbooks.

As mentioned in this thread, please don't forget about your new tools!

i ts nice to have renew trigger surge of light on crit = free flash heal