X-ray scattering methods were applied to the study of thin mosaic ZnO layers deposited by Pulsed Laser Deposition on c-Al2O3 substrates and thin mosaic GaP layers deposited by Molecular Beam Epitaxy (MBE) on Si(001) substrates. For both systems, High Resolution (HR) studies revealed two components in the ω scans (transverse scans) which were not resolved in conventional "open-detector" ω rocking curves: a narrow, resolution-limited, peak, characteristic of longrange correlation, and a broad peak, due to defect-related diffuse-scattering giving a limited transverse structural correlation length. Thus, for such mosaic films, the conventional ω rocking curve Full Width at Half Maximum linewidth was found to be inadapted as an overall figure-of-merit for the structural quality, in that, first, the different contributions were not meaningfully represented, and, second, the linewidth depends more strongly on the film thickness than on the dispersion in the crystallographic orientation or the defect density. A "Williamson-Hall like" integral breadth (IB) metric for the HR (00.l) transverse-scans was developed as a reliable, fast, accurate and robust alternative to the rocking curve linewidth for routine non-destructive testing of such mosaic thin films. For ZnO/c-Al2O3 films of various thicknesses, it was deduced from the transverse scans profiles that this finite lateral correlation length may arise from misfit dislocations which accommodate the lattice-mismatch at the film-substrate interface. This WHL method is shown to be a generic approach applicable to the study of other mosaic, epitaxial, thin-film systems as illustrated through the study of mosaic GaP thin films grown by MBE on Si(001) 4°-off substrates. For this heterogeneous system, it was found from the transverse scan profiles around (002) and (006) that anti-phase crystalline domains can be evidenced. A finite correlation length associated with lateral anti-phase domain size was proposed.