Without hesitation, geodynamic situation strongly influences to hydrocarbon deposit generation and its preservation. For instance, geological conditions in the Dead Sea Basin are very favorable for large oil deposits accumulation. At the same time non-stable geodynamic pattern and active seismology do not assist to hydrocarbon deposit safety. Therefore, several drilled boreholes in this area discovered only signatures of hydrocarbons.
The theory of earthquake generation is generally grounded on the massive fracturing of the rocks under continuous increasing of the pressure. But the volume of the rocks in depth of the Earth's crust is not changing. So, one of the theories gives reason to infiltration of fluids in the fractured volumes (water, oil or gas) and the creation of new stress conditions. Finally, the critical stress creates the conditions for appearance or activation of faulting and the related earthquake process. But the correct question is what follows? The fluids in the adjacent areas to the main fault are they remaining in the created traps or the earthquake is facilitating their migration to some other fractured volumes? You see, the dynamic areas of the Earth are not very known as areas of oil and gas accumulations, but in areas of moderate earthquake regimes the existence of oil and gas field is a fact. For such areas if you overlap the oil and gas fields on the map of active faults, you can see very interesting correlations, not explored seriously till now.
a) the impact of these processes to natural fracture formation
b) to distribution of pressures within intervals of interest
These suggestions consider the geodynamic processes as "finished procedures" or "static states", during an oilfield's production period. I don't think there are geodynamic processes which can affect the recovery in real-time. They do not occur so rapidly compared to the life-time of an exploitation.
The above answers highlight most of the points. But i would like to add one out of the box suggestion. Geodynamics my impact the seal integrity, leading to the reduction of seal capacity and reduction in hydrocarbon column height. This will impact your oil in place.
Also it may impact your hydrocarbon drive mechanism. For example take a bottle of carbonated drink and shack, one you open what will happen? CO2 will separate from the fluid and raped expansion occurs. I think this may happen as well in the subsurface. Dissolved gases may free given a strong quack, creating a gas cape drive? Depending on your well position, you may end up production more gas? And potentially kill the reservoir energy.