I suggest not using a mobile device as your primary means of playing, since there are other features that require you to drag and drop. This game isn't designed for mobile devices and probably will never be fully compatible.
The only other feature I have encountered that requires drag and drop is managing fitouts for NPCs. I tend to use an iphone to log in often and I can't think of anything else that isn't doable. Equipping yourself can be a little tedious, and to move to have to tap a square twice, but other than that it is possible to use a mobile device (iphone at least) for the vast majority of the combine (though as has been stated not recommended).