A: The straightforward answer is yes; you can paint over dirty walls. However, if you decide to do this, you may not receive lasting results, as the sticking ability of the paint will be lessened. For better results, make sure that the walls have been cleaned and prepped before applying a fresh coat of paint.
In general, clean walls take paint better than dirtier ones do. Even if your walls do not look particularly dirty, consider power washing so that all the possible dirt and dust is successfully removed. Make sure to fix any damages on your walls and apply a primer before painting, such as the Dulux Primer & Undercoat for Multi Surfaces.