Leaking shower/tub enclosure
I fixed the problem so I may as well answer my own question.


The spout was detachable from the pipe (it is held on by a mechanism
which can be loosened by a hex wrench -- the nut is on the underside
of the spout)
Once the spout is removed, you can caulk the gap where the pipe goes 
through the hole in the shower enclosure, and then re-attach the 
spout. There's no need to caulk around the spout itself.
I was able to re-attach the spout so there was not such a wide gap
between it and the enclosure, though that's more of a cosmetic
improvement than anything else.


There is a video of someone doing this repair here.