We use the ATLAS3D sample of 260 early-type galaxies to study the apparent kinematic misalignment angle, Ψ, defined as the angle between the photometric and kinematic major axes. We find that 71 per cent of nearby early-type galaxies are strictly aligned systems (Ψ≤ 5°), an additional 14 per cent have 5° < Ψ≤ 10° and 90 per cent of galaxies have Ψ≤ 15°. Taking into account measurement uncertainties, 90 per cent of galaxies can be considered aligned to better than 5°, suggesting that only a small fraction of early-type galaxies (∼10 per cent) are not consistent with the axisymmetry within the projected half-light radius. We identify morphological features such as bars and rings (30 per cent), dust structures (16 per cent), blue nuclear colours (6 per cent) and evidence of interactions (8 per cent) visible on ATLAS3D galaxies. We use kinemetry to analyse the mean velocity maps and separate galaxies into two broad types of regular and non-regular rotators. We find 82 per cent of regular rotators and 17 per cent of non-regular rotators, with two galaxies that we were not able to classify due to the poor data quality. The non-regular rotators are typically found in dense regions and are massive. We characterize the specific features in the mean velocity and velocity dispersion maps. The majority of galaxies do not have any specific features, but we highlight here the frequency of the kinematically distinct cores (7 per cent of galaxies) and the aligned double peaks in the velocity dispersion maps (4 per cent of galaxies). We separate galaxies into five kinematic groups based on the kinemetric features, which are then used to interpret the (Ψ-ε) diagram. Most of the galaxies that are misaligned have complex kinematics and are non-regular rotators. In addition, some show evidence of the interaction and might not be in equilibrium, while some are barred. While the trends are weak, there is a tendency that large values of Ψ are found in galaxies at intermediate environmental densities and among the most massive galaxies in the sample. Taking into account the kinematic alignment and the kinemetric analysis, the majority of early-type galaxies have velocity maps more similar to that of the spiral discs than to that of the remnants of equal-mass mergers. We suggest that the most common formation mechanism for early-type galaxies preserves the axisymmetry of the disc progenitors and their general kinematic properties. Less commonly, the formation process results in a triaxial galaxy with much lower net angular momentum.