My guild has been killing chimaeron25 for a couple weeks. I'm pretty sure 4-5 slimes go out every time. The best way to organize it that we came up with is to assign one healer per group for low health and let the tank healers do their thing(this implies that you should bring 7 healers, you might get away with less at better gear levels but 7 is a good starting point).

This works really well for the priests because if 3 people get hit in your group you can poh to get them all above 10k.
Most of the time you have to heal one person up and sometimes two. Even though other classes don't have group heals like PoH healing up 2 or more people isn't that hard.The big thing is this eliminates overhealing(healing people once they are over 10k) so you can conserve mana for when the bot is offline and you need to crank out heals. Just keep in mind the assignments are mostly arbitrary and it's just a easy way to say I have these 5 people you don't have to worry about them. In 10 man you don't need to do anything as complex and something like Carnathagia suggested works fine.

What we do is, we form a self-healing ranged dps grp, consisting of warlocks, shadow priests and an elemental shammy for healing totem. We give them a lightwell, and they pretty much keep themselves up, without any dedicated healer.
You can have your resto druid be on tank healing, and assist the self-sufficient group when needed.

We are also killing him with 7 healers; the heavy dmg phase is much easier with 7 and there are no dps requirements to drop to 6 healers.

We actually run 8 healers for Chimaeron. If you think about it, it's really not a DPS intensive fight at all. All the work is on the healers. It takes so long for Chimaeron to kill your raid sub 20% with everyone using their proper survival tools, and all the healers are DPS'ing at that point anyways.

We also very carefully coordinate cooldowns for each Feud. Usually we have 5 of them to deal with -- I can PWB 1/3/5 and Divine Hymn on another, while the other disc priest can PWB 2/4 and use Divine Hymn on another.

I find on that fight that the causes of wipes come from 2 different directions. If you're wiping during Feuds, it means you have a throughput problem. This can be mitigated with better use of raid cooldowns, or adding a healer. If you're wiping outside of Feuds, you have an execution problem in healing people up when they get hit by Slime. Tank deaths should be fairly rare.

With 8 healers, we have 2 dedicated to the tank, one healer assigned to each group to patch people up, and one floater. The floater will start at the "bottom" of groups, while the healers assigned to each group will start at the top of theirs. If nobody gets hit from my group, I'll pick another group that has 2 or 3 people hit and start at the bottom as well. This ensures that myself and the healer assigned to that group aren't healing the same person right away.

I think Holy is better at patching people up, but PWB (glyphed of course) is an extremely powerful cooldown on this fight. Feud healing becomes much easier.

One last thing -- remind your DPS that the slime puts a -75% hit debuff on you, so during Feuds hybrids can heal themselves some as well.

We started 25 mans last night, and after breezing through the first three with no trouble, we had to take a few attempts on Chimaeron. We started with a modified version of our 10 man strategy where 5 healers were assigned the 5 debuffs, but after several attempts we opted for the group assignment strategy, which worked much better. I used the suggestions above, such as Binding Heal when myself and one other were debuffed, and Prayer of Healing with 3 of more. Also, often I would save 3 people in a shaman's group with a hasted PoH before Massacre. We started with 6 healers, until we realized we needed more throughput and cooldowns for Fued, and our Shadow Priest switched to Discipline to make 7 (2 Paladins on tanks/support, 1 Druid, 2 Shaman, 2 Priests each assigned one group). Also, this was one fight where Holy Word: Sanctuary seemed to have some use. I usually had plenty of mana going into Fued, but we needed extra throughput to keep everyone alive. However, looking back at the logs how abysmally it performed, I'm not so sure. 121k healing done over the course of 3 fueds is only 1613 healing done per player on each fued, and I don't recall anyone lower than that.

Bring three Discipline priests and use Power Word: Barrier on each pillar. Also arranging groups for Prayer of Healing does indeed help a lot.

Note that Discipline also has the benefit of doing a Borrowed Time + Power Infusion -> Hymn of Hope for basically a full mana bar for the entire healing team.

Are you taking a 3rd Lightning Machine before going into P2? If so have a Disc Priest PWB the raid, and/or D.Guardian the last one to keep everyone a bit more topped off before going to their pillars. I found in 10m that rolling Renews with Heal to autorefresh in Serenity worked great. In 25m I'd imagine Sanctuary and PoM with CoH and PoH would be best. Make sure to have your Shaman time Mana tide with a Spirit proc or clicky on your end.

A better group configuration did the trick. I was able to mostly PoH rather than mostly relying on BH/GH spam. It was still pressing on mana (as it should be) but not impossible. Mana Tide shortly before phase 2 and immediately after it ends helped a ton, also.

We don't have a disc priest for the crackles (I'm holy). Instead we just rotate Divine Guardian and Divine Hymn/Tranq on phase 2 as needed.

It does, and it works perfectly. That same glyph will also work for Guardian Spirit next patch.

Lately I noticed some strange behavior with Mass Dispel, especially on Cho'gall ( frapsed it here YouTube - Mass Dispel fails ), it seems to ignore some targets and I have to cast it 3-4 times until I get everyone out.
Did anyone noticed something similar, or any ideas what could cause this?

Here are some logs from the first 5 Mass Dispels in the video:

The video was uploaded yesterday, but when was it recorded? Maybe this has something to do with the trapdoor issue hotfixed recently?

Mass Dispel has long been wonky in choosing targets that have nothing to dispel on them, while leaving targets in need still inflicted.

This was happening even before the dispel mechanic change (unable to dispel unless there was something you could). It would not surprise me one bit if you were seeing strange targetting issues.

Have you posted that on the bug reports forum?