As there seems to be some support for this suggestion, I implemented the following:
If there is some piece under the cursor point this is selected and one can directly drag it. If there is no such piece, then the area selection is used, i.e. no change is made in this case.
Personally I consider this behavior problematic for two reasons:
1) One can much easier accidentally drag some pieces around
2) In a level which is full of terrain pieces, the area selection is much harder to get. This is partially migitated by the fact, that area selection is always used if Ctrl is pressed, i.e. when the "add pieces to selection" mode is used.
I still can't reproduce the bug with the piece selection outside the level area that Kingshadow3, IchoTolot and möbius encounter.