220VDC motor slow and jerking
Using a straight dc motor for a washing machine drive is new to me.  I'd expect a straight induction motor (likely cap start and/or cap run) or perhaps a universal motor.  The fact that it has brushes means it is either a universal or a dc motor.  In both cases, good brush contact is needed in order to excite the armature coils on the rotor.  Intermittent contact of the brushes will result in intermittent torque.  

The uneven wear of the brushes indicates that they may need replacement. Without knowing the the original dimensions of the brushes, I can't say if 3mm is enough or not, but since you're having problems with the motor, I'll guess its probably not.  

You might also ohmmeter check the armature windings for continuity since there could be a broken connection between the brush contact and winding for example.