A singularity in this context is simply a configuration of the manipulator system in which a degree of freedom is lost.
For example, for the Shuttle and ISS arms, the elbow singularity occurs when the elbow joint angle nears 180 degrees; the degree of freedom lost is the ability to translate the end effector away from the shoulder joint.
The relationship to the question about attitude control is that the software would have to avoid all these singularities if the arm were being used for attitude control. Just as they have to be avoided when the arm is being used to manipulate a payload.
Sometimes in the latter case the arm has to be reconfigured to avoid a singularity, and that sounds undesirable for the attitude control case.
Edit: list of singularities for the shuttle arm
- Shoulder yaw; loss of +/- Y translation
- Planar pitch; loss of translation away from the shoulder
- Wrist yaw; loss of some roll commands