What is wrong with my calculations of Venus' orbital period?
Kepler's laws state that a planet sweeps equal areas in equal times as it moves in its elliptical orbit. It doesn't state that different planets will sweep the same area.

The "equal areas" law can be derived from the "conservation of angular momentum". In fact dA/dt = L/(2m)  (where A is the area, L is the angular momentum and m is the (reduced) mass). 

Different planets will sweep out different areas. To calculate the period you used Kepler's third Law: $T^2 = k a^3$ (T= orbital period,a = semi-major axis). If, for convenience you take a in AU and T in Earth Years, then the constant $k=1$.

For Venus, a = 0.72. so $T=\sqrt{0.72^3}=0.61$ or about 223 days.

Hyperphysics has a section on Kepler's Laws