A stand alone GPS receiver doesn't have an electronic compass. If you mean the additional electronic compass Subsystem on a chip, then these can vary from around +-0.1 degrees for $500+ digital compass systems (for dead reckoning navigation when the GPS signal is unavailable) to around +- 2 degrees for the devices commonly found in watches and $100+ GPS systems such as hand held Garmin units. They also need constant calibration and I have also noticed are subject to electromagnetic RF interference.

If using software velocity filtering to generate a velocity vector (speed and direction) when on the move from GPS data sets recorded earlier in time, then the accuracy will depend on so many variables (is WAAS or EGNOS in use, what is the HDOP (variable with time), the number of SVs (variable with time), the GPS positional data rate 1, 5 or 10 sec or more etc, higher frequency update is better for directional accuracy) that I wouldn't ever really trust the software GPS system to point me in the correct direction. The accuracy of the GPS software compass improves when moving at much higher velocities for example (assuming that the GPS update frequency remains constant). I certainly wouldn't trust a software GPS compass when moving at walking speeds for example.