Transonic flow past a NASA SC(2)-0710 airfoil with deployments of a spoiler up to $6^{circ}$ was studied numerically. We consider angles of attack from $-0.6^{circ}$ to $0.6^{circ}$ and free-stream Mach numbers from 0.81 to 0.86. Solutions of the unsteady Reynolds-averaged Navier-Stokes equations were obtained with a finite-volume solver using several turbulence models. Both stationary and time-dependent deployments of the spoiler were examined. The study revealed the existence of narrow bands of the Mach number, angle of attack, and spoiler deflection angle, in which the flow was extremely sensitive to small perturbations. Simulations of 3D flow past a swept wing confirmed the flow sensitivity to small perturbations of boundary conditions.