Contourf on the faces of a Matplotlib cube

You have to assign the data to the right axis. The zig-zag results from the fact that now you are at x = const and have your oscillation in the z-direction (from the random data, which is generated between 0 and 1).
If you you assign the matrixes differently in your example, you end up with the desired result:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

plt.close('all')
fig = plt.figure()
ax = fig.gca(projection='3d')

X = np.linspace(-5, 5, 43)
Y = np.linspace(-5, 5, 28)
X, Y = np.meshgrid(X, Y)

varone=np.random.rand(75,28,43) * 5.0 - 10.0
Z=varone[0,:,:]

cset = [[],[],[]]

# this is the example that worked for you:
cset[0] = ax.contourf(X, Y, Z, zdir='z', offset=5,
                      levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')

# now, for the x-constant face, assign the contour to the x-plot-variable:
cset[1] = ax.contourf(Z, Y, X, zdir='x', offset=5,
                      levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')

# likewise, for the y-constant face, assign the contour to the y-plot-variable:
cset[2] = ax.contourf(X, Z, Y, zdir='y', offset=-5,
                      levels=np.linspace(np.min(Z),np.max(Z),30),cmap='jet')

# setting 3D-axis-limits:    
ax.set_xlim3d(-5,5)
ax.set_ylim3d(-5,5)
ax.set_zlim3d(-5,5)

plt.show()

The result looks like this: