X-ray phase tomography aims at reconstructing the 3D electron density distribution of an object. It offers enhanced sensitivity compared to attenuation-based X-ray absorption tomography. In propagation-based methods, phase contrast is achieved by letting the beam propagate after interaction with the object. The phase shift is then retrieved at each projection angle, and subsequently used in tomographic reconstruction to obtain the refractive index decrement distribution, which is proportional to the electron density. Accurate phase retrieval is achieved by combining images at different propagation distances. For reconstructions of good quality, the phase-contrast images recorded at different distances need to be accurately aligned. In this work, we characterise the artefacts related to misalignment of the phase-contrast images, and investigate the use of different registration algorithms for aligning in-line phase-contrast images. The characterisation of artefacts is done by a simulation study and comparison with experimental data. Loss in resolution due to vibrations is found to be comparable to attenuation-based computed tomography. Further, it is shown that registration of phase-contrast images is nontrivial due to the difference in contrast between the different images, and the often periodical artefacts present in the phase-contrast images if multilayer X-ray optics are used. To address this, we compared two registration algorithms for aligning phase-contrast images acquired by magnified X-ray nanotomography: one based on cross-correlation and one based on mutual information. We found that the mutual information-based registration algorithm was more robust than a correlation-based method.