My Cessna 150 is equipped with a Bendix ADF, which is deadly accurate within, let's say, 3 NM.
You cannot express the accuracy of an NDB in NM it has to be in Degrees. A good ADF may have a typical accuracy of 2-3 degrees within the protected range of the beacon, beyond that anything may happen. If the needle is wandering, that implies a poor signal level or interference from other signals.
A three position line fix taken from NDBs is much more accurate than using 3 VORs, that's why the military use TACAN as opposed to VOR.
Many non calibrated NDBs at GA airfields use poor quality antennas which do not produce a vertical cone of silence, the radiated signal may be weak and bearings may also be affected.
I recall flying a Piper Dakota away from Filton and the NDB was still rock steady at Enstone.
Another thing you should ask is has the ADF receiver been calibrated; a good ADF compensates for quadrantal error. Has it got a corrector and when was it last adjusted?
When you are over the top of an ADF you know exactly where you are; a GPS may give you the position in more digits but you can never be quite as shure!