little adds are not a huge deal, you should try and pick them up though but make sure you are in place to pick up the bigger adds on each door (for the second set make sure you're right there to pick one up and charge/heroic leap/heroic throw/taunt/etc... to get the second one) as they are way more important. on the 4th door make sure people aren't standing where the bears drop down otherwise they're liable to be 1 shot.
on the third door try to keep people close together so you can get the little adds down better through aoe and not having people spread all over the area. the little adds dot can really start doing huge damage.
the poison adds must be interrupted. that is a huge amount of extra damage going on the raid. make sure you have people assigned to interrupt them. the effusions can usually be killed pretty quickly. The first venom priest should be killed before it summons an effusion and the next set comes down.
After a couple attempts, you'll memorize where the adds spawn (or at least the general idea. The adds from the gate spawn kind of randomly)
what I do is move the adds around where the next 'group' spawns and tank them accordingly.
First small adds, not big of a deal, assuming you dont get stunned by the basilisks (can be interrupted)
second door small add leaves a dot after a charge towards a random member, can hurt a bit and I used safeguard as much as possible for it.
Third dorr, as bals mentioned the adds target/fixate random raid members and cannot be taunted.
For Fourth door, I tank the warbear/shamans and the melee small add, but not the caster small one. Our melee dps took care of that (interrupt and dps)
Now for banners.
I used mocking banner on 2nd and 4th door. 2nd door right before dinomancer pops because thats when the small adds+ Effusion(clones of venom priest) spawns. With disrupting shout +some aoe the clones wont be a problem
For 4th door I use it around when the 2nd group of bears spawn. This is because I have to move out of totems during this time and I don't want to move the bears around too much (cleave).
I have a video in my PoV (also warrior on add tank). The quality is low because I had my fraps setting low and the voice chat is going to be in Korean. But you'll be able to see the 'path' that I tank for each door. Hope it helps.
Super easy as a warrior. If possible, have your raid stay on the side closest to the next door so the adds aggro in that direction. In addition to that warriors will have mocking banner for both doors they tank. I usually use it on the group of 2 special adds that spawn in the area the dinomancer comes as well.