There are also some redraw bugs in there: If I use testcalendar and
turn on "show headings" and "show day names", the arrows are drawn.
Now disable "show day names" again. This causes the calendar widget to
shrink. The month arrows are redrawn, the year arrows aren't and I
have to move the mouse over them to make them reappear.

Here is a patch which makes the arrows insensitive when the calendar
is insensitive and uses style functions for drawing the arrows.

Created attachment 16342 [details] [review]
patch

Any time one touches GtkCalendar, it's hard to tell where
to stop fixing stuff... to get the arrow drawing right,
I think the code should:

 - Make the arrow windows input-only

 - use gtk_paint_flat_box() instead of setting and
   clearing the background of the arrow window

 - Instead of calling gtk_paint_arrow() directly
   in changes, have a gtk_invalidate_arrow() which
   invalidates that portion of the window. The goal
   for all of GTK+ these days is that all drawing
   in done out of process_updates()

That's sort of the minimum to get things to have
a chance of theming nicely.

I'd also comment that it doesn't look like:
 
 gtk_calendar_set_background()

is using the right colors for the arrow windows, but with
the above changes that doesn't matter.

I've committed the patch to get rid of draw_arrow_{left,right} in
favour of gtk_paint_arrow and to fix the appearance of the arrows in
an insensitive calendar. 

Leaving this open to track the more extensive drawing fixes proposed
by Owen.

This should all be fixed