We provide examples on how the non-convexity of the underlying optimization problem can affect the solution to nonlinear model predictive control (NMPC) problems. Using numerical simulations, we show different features of NMPC solutions that illustrate the existence of local minima and their effect on properties such as continuity. It is the purpose of this paper to provide simple examples that can be used to demonstrate all these traits. Furthermore, as the existence of local minima can carry over to the existence of locally optimal active sets, we discuss possible challenges from the perspective of solving the NMPC problem explicitly.