How do I copy something from the curtain?
Short answer: Click a tile in the curtain to copy that scrap, then press ⌘V in the app you're working in — it stays in front the whole time.
Click a tile and that scrap goes onto your clipboard; then press ⌘V where you want it. Because the curtain doesn't take focus, the app you were working in stays in front, ready for the paste.
Images paste as images and file tiles paste the real file. If you want a closer look before copying, click the tile's eye button to open the preview first.