One problem is, of course, the correct specification of the model, i.e. the question if the true model is really linear. In this graphic you can freely choose a functional relation. By default, I have set a quadratic relation. Then, the data will be generated and you can show the true model by clicking the button "show true model". What do you notice about the residuals?
Apparently, in case of misspecified models (black), the residuals are not evenly distributed around the x-axis like the true errors (red), but show a structure. In this example, it is a "smile".