Please supply minimal code examples that illustrate the problems, and specify what is the latest mpl version you have tested. At least the first of the things you mention sounds familiar, and I think it was fixed--but maybe not.

I'm using matplotlib 1.3.1. (I need to find a way how to easily replace that with a newer version.)

A minimal example to reproduce disjoint lines is the following:

import matplotlib
import matplotlib.pyplot as plt
matplotlib.rcParams['axes.linewidth'] = 10

plt.imshow([[1,2],[2,1]])
plt.colorbar()
plt.savefig('test.pdf')

Alternatively omit the first and third line and magnify. Look at the edges of the plot and colorbar.

I'm aware that doing it properly for the main plot could be a bit tricky given that the user can probably switch individual lines on or off. Fixing the colorbar should be straightforward at least.

@mojca, thank you. Both problems are fixed in master.