While kinematical diffraction is adequate to understand the geometry of the diffraction spots, it does not correctly give the intensities and has a number of other limitations. For a more complete approach one has to include multiple scattering of the electrons using methods that date back to the early work of Hans Bethe in 1928. These are based around solutions of the Schrödinger equation using the relativistic effective mass  described earlier. Even at very high energies dynamical diffraction is needed as the relativistic mass and wavelength partially cancel, so the role of the potential is larger than might be thought.
The main components of current dynamical diffraction of electrons include:
* Taking into account the scattering back into the incident beam both from diffracted beams and between all others, not just single scattering from the incident beam to diffracted beams. This is important even for samples which are only a few atoms thick.
* Modelling at least semi-empirically the role of inelastic scattering by an imaginary component of the potential, also called an "optical potential". There is always inelastic scattering, and often it can have a major effect on both the background and sometimes the details, see Figure 7 and 18.
* Higher-order numerical approaches to calculate the intensities such as multislice, matrix methods which are called Bloch-wave approaches or muffin-tin approaches. With these diffraction spots which are not present in kinematical theory can be present, e.g.
* Contributions to the diffraction from elastic strain and  crystallographic defects, and also what Jens Lindhard called the string potential.
* For transmission electron microscopes effects due to variations in the thickness of the sample and the normal to the surface. 
* Both in the geometry of scattering and calculations, for both LEED and RHEED, effects due to the presence of surface steps, surface reconstructions and other atoms at the surface. Often these change the diffraction details significantly. 
* For LEED, use more careful analyses of the potential because contributions from exchange terms can be important. Without these the calculations may not be accurate enough.