I think that time for now should be spent on making the existing bases exceptional rather than new stuff. There's already a couple of community members working on Pet Bots. Leave that alone then adopt the best one later if they'll let you.
There's already been a ton of good ideas but I'll throw some of my thoughts out as well in some semblance of priority.
General Stuff
1. Auth server. Without it doing its job right, the rest of the list is moot.
2. Navigation, navigation, navigation.
- KunLai Summit is impossible to navigate. Other places have similar issues. The bot needs to recognize a mountain it can't climb and stop kissing it while doing the unstuck dance. The thing is "smart enough" to run to across a field and to a road in a place like the Barrens when it doesn't matter but when it does matter it ignores the road and tries to climb up the side of the Himalayas to get to Temple of the White Tiger.
- From the center of Halfhill Market the bot will not only go the long way around to Jogu (over a pot and behind a tree) but if you blackspot the pot and the tree then it tries to try to run over Anthea's semi circle table on the other side of the market instead of around it?! Use the wide open path, dummy!
- Is there any way to make it fly smoother? More arcs and curves instead of snap turns, sharp drops and straight lines?
3. Stuck Handling - Its gonna happen. Could it look a little more human or at least random? (My son actually does the stuck handling dance. He thinks its hilarious. If it can be copied exactly like a dance move in a video, that's bad.)
4. Targeting/Awareness Issues -
Perfectly described by Kamilche Plus:
The ability to control attacking of tagged mobs. I don't want to attack someone else's stupid goats but I do want to pot shot the Hunter Chief or the Behemoth because I'll get credit even if the other guy does the work. As a profile writer I'd like to be able to override the user's choice when its in the best interest of the profile just like other user settings.
Trying to attack opposing faction pets
5. Give me back my two logging tabs!!!! As a profile writer I need to see what my Normal user will see and I want to see the diagnostic but not always together. If I'm monitoring the Normal and something goes wrong I have to open the log to find it instead of just switching tabs and comparing. And while you're at it, could you force line numbers out to the log in diagnostic mode?
6. The Forum - Lock the thing down so most areas are only open to paying customers. Why are we handing out our attack plans for free to the enemy?
7. New Features: If you're gonna go for NEW, go for this.
Display the current profile (or sub profile or subsequently loaded profile) at all times, maybe on the Info tab?
Let me change Combat Routine without closing HB
Pause Button
Blackspot button to write to user's global blackspots.xml
A don't sell/don't mail user setting. If enabled the toon just camps (or hearths and camps. You could even make THAT a choice) If not, the bot does what it does now. Or give me profile tags that can control that.
The built in relog, LogMeOut, login scheduling stuff has promise.
8. While I'm wishing can I ask Santa for a skilled coder mod who covers the Development forum so I actually get help when I ask questions I'm stuck on?

BGBuddy
I have actually never used it. In its current state I never will. I know how much negative attention its bringing the community and attention is bad for everyone. Do whatever you gotta do to get rid of that attention. (And if that makes BG Buddy work better for PvPers that's just bonus!)
Questing Bot
1. More conditional capabilities and the ability to create an option interface for questing similar to what you can fake by wrapping a questing profile inside PB. (If there's a way to create your own bool and have it used in a conditional in a quest profile and I just don't know it would someone please teach me! I'll donate for mentoring!)
2. Make sure the QBs that come packaged with the product actually work after updates (see PerformTradeskillOn)
3. QB wish list:
Could you make the ForcedMount.cs use the user selected mount instead of the first one in the list?
Could you make a KillThings like CollectThings so I have the control of CollectThings but will attack from range?
Gatherbuddy
If I'd been using GB much during MoP instead of indulging my new obsession with questing profiles I'd probably have specifics here for you. Instead I'll just say, if its not doing the job its intended to do in a consistent, dependable and inconspicuous manner, fix it.
DungeonBuddy
See Gatherbuddy suggestion.
All Other Bot Bases and Anything I Missed
See Gatherbuddy suggestion.
TL;DR If its not doing the job its intended to do in a consistent, dependable and inconspicuous manner, fix it. (and help Makkli learn to code)