Rad Roaches and Molerats that spawn in empty rooms leave far too quickly. Too often it is impossible to move someone in before they leave. Even worse is the fact that they multiply. Because of this it makes the game far too difficult for new players who haven't gotten many weapons for their vault yet or have recently lost characters in the game. If you have 2 rooms next to each other that are empty this can cause a chain reaction. Such a chain reaction can make it nearly impossible to recover from a difficult fight.
Stimpacks are nearly useless during a combat in the vault. With the exception of fires, any situation where they might be necessary results in vault dwellers standing on top of each other preventing you from selecting them to be healed. Either they should be used automatically in the vault when needed, or you should allow the player to just click on the room where people need healing and have it happen automatically.
Likewise, rooms with stations at different depth often make it nearly impossible to select or grab people. Normally this is simply obnoxious, but in the heat of battle it can be devastating. Rather than clicking on the figure, just pull up the list every time we select the room, and let us drag from the list instead. This would streamline the process so much in a touch scenario. This also gets in the way of selecting a room which is populated as you often end up selecting just a person inside.
In combat there is no rhyme or reason to who replaces who when you drag people into a room. Instead of prioritizing stats, in combat you should prioritize who has the lowest health or does not have a weapon. This would help greatly.
Better yet, instead of dragging a person, let us touch them and then touch the room we wish them to go to. I have terrible trouble with touch drags on any device where unless I jam my finger on the screen, sometimes the screen registers my drag intermittently. I use the touch and place method as my preferred method in Plants vs. Zombies 2, and I see no reason why you shouldn't implement it here.