Lattice Pathologies
Lattice pathologies lead to features in diffraction images that are not explained by straightforward Fourier transform of the contents of the unit cell, sampled at its reciprocal lattice positions.
One example of this is Incommensurate Modulation (for examples, see the PDF of 2nd reference in article Incommensurate Modulation).
Other reasons are:
lattice-translocation disorderEdit
An intermediate type of disorder with partially coherent interference between crystal domains related by non-lattice translations. A recent paper on the subject is Acta Cryst. D65, 980-988 (also see the references in it). This type of disorder has a long and distinguished history in protein crystallography, starting with a paper by Bragg & Howells (1954) Acta Cryst. 7, 409-411.