I have been playing fallout shelter for nigh on a month and I have encountered next to no bugs. It runs very smoothly on an iPhone 6. However, I have encountered a small but very irritating glitch that is preventing me from getting a certain Lunchbox. The glitch goes as follows:
The quest is something along the lines of "raise the x skill of y dwellers". In this case it was the Luck special, and I had to increase it for 7 dwellers. I put six characters in a 3-room Game room. I waited patiently and eventually all of the dwellers had little green cats (the symbol for luck upgrades) above their heads. I collected all six and waited for the next batch, about three hours. At this point, I was hoping to find something cool in the lunchbox from the quest. Some power armor, for example. When the time came I tapped on all the cats in quick succession, only to find that the quest bar did not go up to 7 of 7 and instead stayed at 6. I waited again and tried. It still didn't work. This had happened previously to me with a Strength increase quest. I ended up having to delete that one to make room for more quests.
To summarise: The quest was to raise the skill of some dwellers. In my case it was the Luck of 7 dwellers. Went to 6/7 easily, and tapped the next luck Icons when they showed up. It gave me an increase in the dweller's luck but nothing in the quest bar. It had happened previously to me with strength and I had to delete the quest. Tried again a few times and nothing happened.
If anything similar has happened to you or if you know how to fix it, please comment. Thank you very much for your time.
-Philip
Note* The issue has been resolved thanks to the community. However, if anybody else has been experiencing this problem, the solution is: You need to improve the skill of seven DIFFERENT dwellers. Kudos to HolyGRUNTY101 for helping me out.