Polarised microscopy is shown to be a powerful alternative to light scattering for the determination of the viscoelasticity of aligned nematic liquid crystals. We perform experiments in a wide range of temperatures by using an adapted version of the recently introduced differential dynamic microscopy technique, which enables us to extract scattering information directly from the microscope images. A dynamic analysis of the images acquired in different geometries provides the splay, twist and bend viscoelastic ratios. A static analysis allows a successful determination of the bend elastic constant. All our results are in excellent agreement with those obtained with the far more time-consuming depolarised light scattering techniques. Remarkably, a noteworthy extension of the investigated temperature-range is observed, owing to the lower sensitivity of microscopy to multiple scattered light. Moreover, we show that the unique space-resolving capacities of our method enable us to investigate nematics in the presence of spatial disorder, where traditional light scattering fails. Our findings demonstrate that the proposed scattering-with-images approach provides a space-resolved probe of the local sample properties, applicable also to other optically anisotropic soft materials.