The cues are a result of
depth. You have given them up, by-definition when you use a flat design.
edit:
To enumerate some of the affordances you lose and problems:
-What is a button? What can I interact with? A raised button used to be a good cue.
-Is that toggle on or off (depressed or no)?
-What is clickable?
-What is important? Closer things used to be more important.
-Is this a "thing" or a word? Shadows used to hint at this.
-Is this a banner or a button?
-What did I click? I don't even know!
Non-flat designs work because they use real world metaphors to build a natural vocabularly that is almost universally understood by our common experiences living in a 3D world. Now, perhaps you can re-define this naturally shared design vocabulary in the flat world. But the point is, you are redefining something which people intuitively already know, and when you have to teach users your interface, that is never as friendly as when they know how to use it intuitively.