Affordable Rock Removal
Tap on any building you want to build. Next, you'll need to choose where to place it. Instead of selecting an empty space, eliminate rocks until you have almost no money left. Now go ahead and place the building wherever you like. The rocks should still be gone but you won't have to pay for their removal.
Infinite Lunch Boxes and Money (Exploit)
This exploit requires you to start a game with a brand new vault. Place the rooms you start with, and have the Dwellers occupy them. Complete objectives from there, until you are asked to either "Equip 1 Dweller With a Weapon" or "Sell 1 Weapon or Outfit." Instead of completing either of those objectives (by claiming a reward), which will disable the exploit, complete other missions until both of the aforementioned objectives are listed. From there, you should soon see a mission to "Get 50 Water," or to "Get 50 Food," or to "Level Up a Dweller." You can complete any of these three missions repeatedly, as long as you have not first completed "Equip 1 Dweller With a Weapon" or "Sell 1 Weapon or Outfit" already noted. Completing those repeatable missions is an easy way to quickly amass a pile of lunchboxes and coins.
Time Lapse (Exploit)
You can change the time on your device to advance the game so that you don't have to wait. You can do so by heading to Settings > General > Date & Time and disabling the Auto option. Note that sometimes this will cause errors when you return to the actual time, so make sure that all rooms are ready to be collected before you restore the settings.
Affordable Rock Removal...