The stability of periodic two-dimensional waves on a liquid film falling down a vertical oscillating plate was studied experimentally using the aqueous solutions of carboxymethylcellulose. A set of capacitance probes was used to measure the instantaneous film thickness. Artificial flow fluctuations induced by the plate oscillations caused distinct intensification of the wavy flow. We use the methods of phase space reconstruction and deterministic chaos analysis to show that the dynamics can be understood within the framework of deterministic chaos. We find that regions of relatively ordered and more complex chaotic dynamics alternate as the frequency of oscillations is varied. There are particular oscillating frequencies at which the system is close to a three-frequency quasiperiodic motion with the spectrum of Lyapunov exponents of type (0, 0, 0, -, ...), elsewhere the system is either in a simple chaotic mode with the spectrum of type (+, 0, 0, -, ...) or in a hyperchaotic mode with spectrum of type (+, +, 0, -, ...).