AOA and camber are small: such that all angles are linearized ( $\sin\theta \approx \tan\theta \approx \theta$) obviously at large angles, this assumption breaks down and the results are worthless.Camber is close to the chord: such that the vortex sheet is assumed to lie on the chord while resulting in the flow path that lies on the camber line.Airfoil is asymptotically thin: such that the mean camber line represents the flow path.Thin Airfoil Theory produces a beautiful result that relates the zero-AOA lift to the mean camber of the airfoil, as well as the lift slope vs AOA of any thin airfoil is $2\pi$.
