I'm working with two RFID readers in my circuit and an arduino to control both of them. The whole thing is powered by a very cheap wall-wart Power supply at 12V which is rather noisy to begin with. And a 7805 Voltage regulator to drop the voltage to 5V for the arduino.
All components have proper decoupling capacitors (in my opinion): 470uF+100nF for the two RFID readers, in close proximity. 100nF for the Arduino (not counting the decoupling on the arduino itself) 22uF+100nF on the input for the 7805 and 100uF+100nF on the 5V output. There is one additional component which is a MAX232 which is set up according to the datasheet.
Therefore I'd say, the decoupling is done porperly. However sensitivity aka read range is 5mm with the wall wart. Now if I use my bench-top Power supply (Peaktech 6150, not even an expensive one) read range is around 55mm. The same effect can be had when connecting the scope to the circuit and using the wall wart. So I'd conclude it is not a problem with the noisy wall wart but rather a problem with the grounding as the bench top PSU and the Scope are probably connected to earth(?) and thus provide a "harder" ground I guess?
Update: Using a scope to probe the 0V or +12V (and any other point) with referenece to the scopes GND, revealed that there are two major components of common mode noise: 355V Pk-Pk @ 50Hz from Mains 10V Pk-Pk @ 125kHz from the antenna-drivers (same frequency).
Probing the +12V point with reference to the 0V on the PCB shows 140mV Pk-Pk @ 1kHz which I belive to be the switching frequency of the wall wart. Superimposed I can still observe some noise from the antenna driver at the same 125kHz but now with the scopes earth/gnd connected it's around 4mV Pk-Pk. Which is sufficently low to bring the read range up to where it should be.
Solution (sorta) An accepted solution would be the use of a pre-made power supply with DC 0V connected to PE directly or via Capacitor. Or some other means of grounding the 0V line. However as Andy aka points out, it would be better to take a look at the susceptibility and source of the noise as this is just a fix for a non-ideal circuit.