A lot of people were excited to see Serendipity when it was first unveiled. It seemed to be Blizzard's answer to mixing up healer rotations, to let healers do things besides spamming one heal. But does it accomplish its purpose?
Serendipity builds up a stacking haste buff when you cast Flash and Binding Heals, that will speed up your next Greater Heal or Prayer of Healing up to 36%. That's a lot of haste; it basically will speed up the GHeal or PoH up to Flash Heal speed. Naturally, this will only be useful if you'll have reason to cast Flash Heals as well as use a big heal nuke from time to time. It's not like the old Improved Holy Concentration which let you simply spam GH and end up hasting a bunch of them.
So where is Serendipity powerful? For tank healing, it does not seem especially useful. One could throw in Flashes when a tank is mostly topped off, to provide a periodic haste buff to GH, which of course is never a bad thing. But where this talent really shines is in conjunction with PoH and Ulduar's raid damage. Prayer of Healing is very powerful targeted group heal. With even 1 or 2 points in Serendipity, a priest can "charge up" their PoH in advance, in preparation of an upcoming Tympanic Tantrum or other burst of AOE. This allows the PoH to land much sooner after damage hits, which also gives all healers more breathing room to top the raid up afterwards.
Serendipity has great synergy with Surge of Light. When assigned to raid healing, there is not always occasion to cast Flash Heals, especially when movement is necessary. But with SoL (proccing off CoH and PoM), there is almost always an opportunity to cast an instant Flash and refresh the Serendipity stack before it expires.
I feel that Serendipity is a useful talent in any environment with raid-wide AOE. It provides a good insurance policy, so that with a little planning, a large heal can be at one's fingertips at a moment's notice. In this way it can serve a role like Borrowed Time does for Disc priests.
The only thing I feel is missing is a good AddOn to track Serendipity's status, since you may wish to see the umber of stacks (to estimate PoH's current cast time), as well as the remaining buff duration (to know when to refresh it, if it will be needed soon).