Downloading all App store purchases? So there is no "good" way of seeing all my purchased items in iTunes (only the very cubersome "purchase history" screen). Is there, however, a way to download all my purchases to the computer? e.g. when I install iTunes on a new computer?

There is the store/check for available downloads button. However, it has no effect in my computer and I suspect that it's not intended for apps, but for music/videos purchased from iTunes (which are not available at my country).

Is there another way? Maybe even an external application?
Unfortunately there is no easy one-click solution to downloading all your previously purchased apps.  Best you can do is look through the list of purchased apps and re-buy them (you will not be charged again).