I have trouble dragging the little dwellers across my phone screen over the expanse of my 40 room vault.
So I thought this might help:
[1] The window you get when you tap a dweller (the one with the stimpacks, radaways, weapons and clothing) has a SELECT button.
[2] When you select a dweller their icon appears over the cog in the top left corner.
[3] When a dweller is so selected, you can't select any other dweller.
[4] This means you can tap / select a dweller and then scroll to a location in the vault without accidentally moving other dwellers.
[5] When you've found the location you want, you can drag the dweller from the cog into the room you want.
[6] If you want to deselect the dweller, tap the dweller in the cog or in its current location to bring up the dweller window, and tap the RELEASE button (which is what the SELECT button turns into when you selected the dweller).
What do people think?