I have created a linear model in R, and then plotted the residuals. If my residual plot looks like this, then which model assumptions are not appropriate?
There might be some heteroskedasticity, since for lower x values there is a much larger (vertical) spread in the residuals. Also there is maybe curvature in the plot, for x larger than about 9 all the residuals are positive, while for lower x values (around 4 to 7) most are negative. To get better advice you need to tell us more, what is the context, what is your variables, what is your modeling goal?