I have observed in many experiments on collisions involving rods of varying densities that the momentum seems to first be conserved only at the point of collision then about the centre of mass. Is my reasoning correct?
Momentum is conserved for any system whereas there are the net forces from outside of the system are zero. If you only consider a small part of the rod, it is hard to keep track of the internal forces in the rod, and you would not be able to say that the momentum is conserved. If you consider the full rod and particle system you can figure out that momentum is conserved.
Note, if the rod is attached to something, for example a wall or a hinge, we do have forces from outside of the system, and momentum will not be conserved in general.