I'm a Holy Priest almost ready for End Game. I checked out the spec you suggested, and it's close to what I have now. In my opinion, Mental Agility isnt THAT big of a deal, for I dont have too many instant casts, let alone any I use in battle. Same with Renew. I use them out of battle, which means I can drink right after if I need too.
http://www.worldofwarcraft.com/info/classes/priest/talents.html?5052300032001000000000205050032300150530150000000000000000000000
Thats my spec as of right now. Works great, never had an issue or complaint.
Why did you put points in Improved Inner Fire and Mental Strength and skip Inner Focus? Improved Inner Fire is almost worthless because, even if it Improved, you won't really change a one-shot situation into a two-shot situation in raids. When I get one-shot, it's normally for like 10k, so adding a little extra armor won't make me live.
Mental Strength is also something that looks good on paper, but isn't worth the points. I use to have it, and with my gear where it was, I had about 13.2k mana raid buffed. When I got rid of it, I dropped to just over 12k mana raid buffed. So, what does 1.2k mana get you? About 2 casts of a Greater Heal (depending on what rank you use). I traded those 5 points to go 23/38 and get Holy Concentration. A single proc of Holy Concentration, even if I'm a complete idiot and don't chain it with Inner Focus and/or the Earring of Soulful Meditiation, it single handedly replaces half the mana. If it procs more than once in a fight, or I chain it with Inner Focus and the Earring, I get WAY more mana than I lost.
In your case, you only have one point in Mental Strength, so it's WAY better spent in Inner Focus. Inner Focus is one of your most powerful mana conservation and regen talents. Here's how I tend to use it. I cast until Holy Concentration Procs, if it's really early in the fight and I'm still at 90%, I ignore a case like that, since it tends to proc at least once every two minutes. When it procs, I wait to go OO5SR and hit my Earring for 300 more spirit. I'm now regenerating with over 1k spirit, or well over 600 MP5 pre 2.4 or well over 1k post 2.4. I now cast/cancel max-rank GH on the MT until he needs it, or Holy Concentration is about to run out. I then hit Inner Focus and continue cast/canceling max-rank GH. That uses up the Inner Focus and I begin cast/canceling one more time. I can usually pull this off for anywhere from 10-20 seconds. Using this, I can regenerate about 3k mana pre 2.4 (not counting Shadow Priest, Totems, or Innervate) while still landing 3 max rank greater heals, one of which has almost a 50% chance of procing Inspiration. If you don't have an Earring, there's another trinket from Bot (I think) that does 130 Mana. Even if yo udon't have a spirit trinket, it's still WAY more mana, especially considering the buff to spirit in 2.4.
Also, why do you bother with Holy Reach? If you're healing, you don't cast Holy Fire or Smite, at least not enough to warrant extending their reach. You're not even specced for Holy Fire or Circle of Healing, so it's really only effecting Prayer of Healing. So, do you really use it enough, and find that your part is THAT spread out that it's worth it? I cannot see justifying any points there unless you have Circle of Healing, which makes it pretty much mandatory.
Also, why do you have a point in Blessed Resilience? Are you getting hit enough to make getting crit a lot a real concern? It's a talent aimed toward deep holy PVPers, and it's a complete waste in PVE.
Further, if you're going 40 points into Holy, why NOT get Circle of Healing? It's an amazingly useful spell, if only situationally. The only reason to justify not having it is for IDS, but since you don't have that, I don't see why you wouldn't put in one more point for it.
For the case for Renew, you're right, it's not that useful pre end game, but it's enormously useful in many situations, particularly in raids, in ways where it's not apparent. If you're MT healing, a renew helps smooth out the spikiness of GH chain casting and increases your total HPS out. It's highly mana efficient if you can all it to tick. I also like to place it on raid members who can wait a few ticks to be topped off, or regularly take damage (Shadow Priests using SW:D and Warlocks Life Tapping) so I can use a GCD on them when I have one to spare and otherwise focus on my primary task. Not having CoH in my build, I find that Renew makes up a very sizable chunk of my healing but only when I learned to use it in the appropriate situations. My tank and raid healing would suffer greatly if I didn't have that talent. It really is fundamental to any Holy Priest build.
Finally, as for the case for Mental Agility, if you're a priest not using instant casts, you're not utilizing your tools effectively. It effects: Power Word: Shield, Power Word: Fortitude, Divine Spirit, Renew, Prayer of Mending, Circle of Healing, Dispel, Abolish Disease, Shadow Word: Pain, Shadow Word: Death. In any given raid, I use all of these spells repeatedly (except for CoH, since I don't have it). ALL of these spells benefit from Mental Agility. In fact, the only spells I use that aren't instant casts are Greater Heal, Binding Heal, Flash Heal, and Prayer of Healing.
If you're not end-game yet, you may not realize the importance of mana efficiency, but it's vitally important to longevity, particularly in long boss fights. Many boss fights at the Tier 5 level will last 8+ minutes, Vashj and Kael alone can be as long as 20 minute boss fights. So, sure, in instances, and many heroics, you can pretty much spam heals and not have much concern for mana, but that just is less and less the case the farther along you get farther along. Although, with the spirit buff in 2.4, you'll regen a lot more so you won't need as much efficiency.
FWIW, I had a spec pretty different than I do now, but the more I experimented and got closer to my current IDS spec, the more I increased my total healing output.