Alright, so I tried Version 0.4 on my Windows machine and this time I manage to complete mountain (and the two before it) with no issues whatsoever. I haven't tried peninsula yet, but I'm pretty confident it'll work as well!
So: Yay for no getting stuck!
Good job!
I'll try: As I said, at some point during the second stage, the game gets stuck. I can select and "place" buildings, but nothing happens (they become green aka "I fit here" and show me how much I would earn). I am still holding the building, no currency gets deducted from my funds, and nothing gets build. As if I hadn't placed it. Selecting a different building and/or spot makes no difference.