Transparency on different systems

Was talking with a friend about transparency of 3d objects on different systems, he mentioned that you need to be "careful" on iOS and Android but couldn't be specific as to what being careful meant (frustratingly helpful, wasn't he?).

So my question(s): Do handheld devices use transparency differently? If so, how so? Are there extra draw calls involved? Is it more cpu intensive? Is there any issues across all platforms I should be aware of when dealing with transparent geometry?

Right now my world is based in a "dreamscape" and as the world around you loads it slides/bounces/jumps in to place. As the items are shifting in to place they begin at a distance completely invisible and "phase" in to place to become solid. So imagine a tree falling from the sky, hardly visible at first then as it reaches its target destination it becomes more and more solid, finally landing and doing a little bouncy settling in.

I am programming for pc / web player at the moment but wish to have it on handheld devices eventually, I need to know if those devices have issues I should be aware of before committing to coding it.