One of the problems with dynamic stability is that there are at least two equations defining the dynamic stability factor and both of them include terms which are hard to quantify with certainty. I don't think it is the maths that lets us down but our inability to accurately predict the dynamic terms such as Magnus moment and pitch damping. Take the Magnus force for instance, at low yaw angles it can completely change its direction let alone its magnitude, so trying to predict that reliably is a problem. Aerodynamic hysteresis can also lead to changes in Magnus moments at the same projectile yaw angles.
In addition the value of the dynamic stability factor for satisfactory stability will vary depending on the value of the gyroscopic stability factor, as shown in the classic stability diagram where Sg and Sd are plotted against each other. A value of Sd of 1 is what is wanted. getting it is not always possible, but other values may be satisfactory depending on Sg.
Though there are no hard and fast rules for dynamic stability we can say that certain features appear to make it worse. Boat tails for instance are usually bad for dynamic stability so the smaller the boat tail the better it will be. Keeping the projectile as short as possible and the CG as far back as possible helps as it reduces the Magnus moment which is what limits bullet total length. Strangely having a hollow in the base of large calibre rounds was found to have a negative effect on dynamic stability. It is also beneficial if the aerodynamics can be kept consistent so sharp angular changes in shape, at the start of the boat tail for instance, instead of curves. But ultimately it is a balancing act between the lift coefficients, the moments of inertia and the damping terms.
Dynamic instability can be a disaster for a projectile but it does not have to be. Many projectiles including artillery shells are dynamically unstable during some part of their flight and yet they still perform in a satisfactory manor.
