The board can operate on an external supply of 6 to 20 volts. If supplied with less than 7V, however, the 5V pin may supply less than five volts and the board may be unstable.
You can run it on 5V using the vin pin (as long as its a regulated input - e.g. Batteries or a wall wart) - it needs the extra voltage as it has a voltage regulator on the board that consumes 1.2V of the input voltage.
The fact is that the wall wart isn't really a regulated supply ...
Certainly some are. And some are not. So be sure about the particular wall wart in question. Wall warts like this one are usually plenty good to connect directly to the 5V pin (not to the Vin pin).
I can directly go with 5V input.
I am not going to use a ready-made Arduino board, so my question was: Build a DC-Input e.g. 7-12V with a 7805 regulator or similar, or go with a MicroUSB port and some external 5V power source? This thread seems to suggest the latter.