Quantification of parameters such as size, kD, second virial coefficient B22 or A2, and zeta potential.
Measuring how these parameters change with dispersant (ionic concentration and pH), will inform under what conditions your material is stable, i.e. size is constant over time, highly positive or negative zeta potential, positive kD and A2 all suggest a dispersion is stable.
Many of these parameters could be measured by light scattering, with the Malvern Zetasizer offering the ability to measure all of these, but other techniques like NTA or Taylor Dispersion may also be of interest.
If you have a mixture of monomeric material and aggregates, then separation by SEC or another technique may be useful.
This is not an easy question to answer and Alex has provided an excellent start. ISO TC24/SC4 Particle Characterization has been working (WG16 and WG17) on such matters for a long period of time (as has TC229, I suspect). Join the standards bodies and assist!