Dear lord, make a freaking pause button.

Trying to sort out all the misc people as to where they need to go next (for stat increasing, moving out max stat dwellers to new locations and replacing them with a new one) and sorting out equipment (going through all the new stuff in inventory and replacing old stuff on dwellers while selling off useless items) is SERIOUSLY annoying when rooms keep spawning resources (so you can't select dwellers there until you harvest), raider attacks drag your POV off (and babies, please put in options to have these events NOT move POV) along with all the other things that go on that, for some reason, you felt were important enough to interrupt the things I'm trying to get done.

And, of course, trying to get dwellers to cover fires and roaches fast when all the above happens.

Putting a pause button in would make all those VERY annoying/frustrating issues go away.

Is it really that bad? I think you're exaggerating. Sure when you load the game after not playing a while you get a lot of stuff to do. Unless you produce barely enough resources you can just ignore collecting them a while, and it's just 1 extra tap if you want to move a dweller from a room with produce. Incidents only happen once in a while and can be handled quite quickly. You can only have 200 dwellers total so can't be that many babies really. Just go to the menu if you need a break. Otherwise go play a turn based strategy game or something if you can't keep up...

Um the home button?