Awesome! I have been running HB for about a week now i think and have been encountering these problems. I have found that most of the time it is with Neutral mobs.
Quests that I have seen (and trying to remember). Playing as Horde so obviously only posting the Horde quests.
Borean Tundra:
Bring 'em back alive
http://www.wowhead.com/quest=11690/bring-em-back-alive
Into the Mist
http://www.wowhead.com/quest=11655/into-the-mist
Patching Up
http://www.wowhead.com/quest=11894/patching-up
Pollen from the Source
http://www.wowhead.com/quest=11717/pollen-from-the-source
Neutral:
Hampering Their Escape
http://www.wowhead.com/quest=11617/hampering-their-escape
Has the questitems but not using them as you said
The Lost Spirits
http://www.wowhead.com/quest=11607/the-lost-spirits
With TLS i found the bot to stand in between 6 of those creatures with 6 questitems required and 3 Craftsman saved and 1 Shammy. But it stood there doing nothing... I watched it for a few seconds as i was checking inventory to see if i had the questitems and i checked the quests. So i don't know if there is a CD issue on when he will use an item or if the bot is confused or if it is due to the bug on Blizzard's end.
DragonBlight:
Planning for the Fute
http://www.wowhead.com/quest=11960/planning-for-the-future
With that quest there is not running around aimlessly but I almost any class i play is running directly to the pups, gets attacked and then uses an AoE spell because it will see the neutral ones as enemies or something. I don't know if it is possible to pull from a 30 yard range or make the target on the enemy mobs first. It looks a bit odd if you need to clear 4 camps but you kill everything every other camp. Since it is a daily it might be easy to check that one.
Grizzly Hills:
Supplemental Income
http://www.wowhead.com/quest=12436/supplemental-income ((Killing worgs and skipping the Stags/Deer/whatever))
Eyes Above
http://www.wowhead.com/quest=12453/eyes-above
I think this quest is working but it takes forever to get it done i think. Seems to only target flying eagles for some reason ((EDIT: My character just did this quest and it went fine.earlier it was dodgy though so am not removing the line))
Flamebinder's Secrets
http://www.wowhead.com/quest=12256/the-flamebinders-secrets
With this quest it is attacking the Huscarls and not the casters that drop the actual item. This results in a lot of running around and getting the questitems on accidental aggro pulls. Due to the bug on Blizzard end maybe it is possible to do something with the hotspots. Normally the casters are around the big cauldron in the center. Then again.. if 10-20 bots lining up at the same spot for quest mobs... easy pickings for bans.
The Unexpected Guest
http://www.wowhead.com/quest=12195/the-unexpected-guest
Neutral mobs. Running around but not attacking them
The Damaged Journal (Horde)
http://www.wowhead.com/quest=12026/the-damaged-journal
The Damaged Journal (Alliance)
http://www.wowhead.com/quest=11986/the-damaged-journal
(Am guessing the Alliance version is the same thing, bot not gathering plans. Just walking in a strange pattern)
Neutral:
Raining Down Destruction
http://www.wowhead.com/quest=11982/raining-down-destruction
Bot will continue to the dwarves to attack them instead of collecting boulders and throw from above.
I hope this is helpful. I added the links because...I don't know. Maybe gives you more insight and might save you some time. I tend to be around the pc when i am botting and am not 100% AFK. but at times it might take me a while to catch the bot doing something strange. At times i am watching a movie and got the game sound low. Checking every 15-30 mins. So there might be some quests that I am missing. IF i spot more quests I will just come back.