Thanks for the detailed report. I can reproduce this.

For the time being, here's how you can somewhat work around this:

import numpy
from matplotlib.colors import LogNorm
from matplotlib.pyplot import pcolormesh,colorbar, rcParams
rcParams['xtick.minor.visible']=True
rcParams['ytick.minor.visible']=True
data = numpy.random.random((10,12))*100.0+0.1 
img = pcolormesh(data,norm=LogNorm())
cbar = colorbar(img)
cbar.ax.minorticks_off()

I just upgraded to matplotlib 2.0.1, and I still see the behavior described by PO.

FWIW, this issue is still present on Matplotlib 2.1 (and master 2.1.0.post357+g075618bb4). (@phobson's workaround is still fine though)

Basically, the issue seems to be that when using a logarithmic-locator like LogLocator or SymmetricalLogLocator, the minor ticks are emulated with non-labelled major ticks, while the minor locator of the colorbar Axes remains AutoMinorLocator but is not visible by default. Except for example when one asked to make every minor tick visible through rcParams tweaking 😈...

This has been fixed by #9903.
Here is a figure obtained right now using the master branch:

Great!