1. I can only speak for myself, but I like to keep track of who is "together" and what children they've had. When you tap on a dweller it would be nice to have a "See Family" button. Either that or when you tap on a dweller all other dwellers have a green outline for go ahead and mate or a red outline for cannot mate. Something!
2. We should be able to name our rooms. That would come into play with a new "Assign To" button. You could tap on a dweller, tap Assign To and then choose your room.
3. List needs to be revamped. We need a better way to sort to prevent endless scrolling. Also, when you're viewing weapons and outfits the lists should be stacked. There should be a "Sell" button at the top then you could select anything you want to sell (multiple items) and when you tap done, those items are sold. Either that or a swipe to sell function. I also want to see which weapons and outfits my dwellers have without tapping every single dweller.
4. More rooms. This is coming but I want to see more. I like the idea of the crafting room and barber shop but I hope there are more. I also wouldn't mind having a Hallway (for those of us that like to space things out).
5. I feel like having rooms to train all SPECIAL stats are cool but how about this? For example, the lounge and game room. Instead of just training Charisma and Luck how about actually using those rooms to raise the happiness of dwellers that need to take a load off. Also, how about being able to assign dwellers to work those rooms?! Bartender, card dealer, etc.
6. Better use for Charisma and Luck within the vault. Maybe it's just me but I find both of these stats useless right now.
7. I touched on this a bit but more ways to raise happiness other than mating, being pregnant and pets.
8. Conversation log. Sometimes it's fun to see what a dweller has to say but we can't monitor all conversations. How about if you tap on a dweller you can see the last five or so things that they said? You can use this to see why a dweller may be unhappy and what would raise their happiness.
9. Wasteland challenges and the ability to assemble a group of dwellers to go out together. Maybe 3-5 per group. Also add this to the "Assign To" button I mentioned earlier so you don't have to drag a dweller to the Wasteland.
10. I HATE having to tap on each room to collect resources and every single dweller to level up. It would be cool to have either in game notifications that alerted you that resources were available and when you tap the notification, you collect it. I can see how that would get annoying so maybe it would be better to have a stacked lost of all of your rooms and it would show you how long to the next resource. If it's available it would be a tapable button. Same with level ups for dwellers.
11. A button to tap to turn away a dweller at the door.
Other things I've seen out there are things like a trading caravan that you can trade items with and the ability to raid other vaults. What do you guys think??