In order to achieve high-precision three-dimensional (3-D) imaging with an airborne downward-looking linear-array 3-D synthetic aperture radar (LA-3D-SAR), a uniform virtual antenna array can be obtained by aperture synthesis of the cross-track sparse multiple-input-multiple-output array. However, the actual 3-D imaging quality is unavoidably degraded by array errors such as the multichannel amplitude-phase errors due to the nonideal antenna characteristics, and the virtual element position errors due to vibrations and motion measurement deviations. We investigate the effects of these errors on the forms and the degrees of image quality degradation and consider the use of corresponding calibration methods to eliminate the effects of errors. For the multichannel amplitude-phase errors, the target response is subject to an integrated sidelobe level increase introduced by the phase error, which can be calibrated based on external (parallel or point target) calibrators, as proposed in the paper. For the virtual element position errors, they mainly the result of contrast degradation and noise in the image along the cross-track direction and have little impact on the range and along-track directions. The imaging performance is more sensitive to the error component in the height direction as compared to other components, the precision requirement of which should be established as the calibration reference. A calibration method based on time-divided active calibrators is proposed to estimate and correct the virtual element position errors. Both numerical simulations and real data experiments have shown the validity of the analyses as well as the effectiveness of the proposed calibration methods.