After some more persistence and patience, I seem to have it running ok on Ubuntu 16.04. I installed it into a fresh anaconda environment using
conda install ~/Downloads/csd-python-api-1.0.0-linux-64-py2.7-conda.tar.bz2
and some simple things work. My initial thought that it wasn't working was because
mol_checked = engine.analyse_molecule( mol )
seemed to hang - that's where the patience came in. It just takes quite a bit longer than I thought it would.
My experience is that using pip install and setting LD_LIBRARY_PATH as suggested in the installation instructions is a mistake. On my machine, at any rate, this left me with incompatible libraries in my the search path, which had been built with an older glibc than the system libraries, so I got a lot of shared library errors. Installing with anaconda didn't show this effect, for reasons that I can't fathom.