What I wrote in Slackware Diary – 3 about keeping Slackware up to date is not correct:

slackpkg update gpg
slackpkg update

Does not do the job. A closer look at told me that I had to also run

# slackpkg install-new
# slackpkg upgrade-all
# slackpkg clean-system

as root. This failed with

FATAL! There is some problem in packages database
       or maybe an installation or upgrade in progress:

LinuxQuestions.org suggested an alternative. I downloaded mirror-slackware-current.sh and modified it to my own needs as mirror-slackware-gtm.sh with
ARCH=${ARCH:-"x86_64"} and RELEASE=${RELEASE:-"15.0"} and ran it. Then, as root

mirror-slackware-gtm.sh
cd root@Tyrone:/home/ftp/pub/Linux/Slackware/slackware64-15.0/slackware64
upgradepkg --install-new */*.t?z

which ran just fine. A lot of output flew by on the screen, but

cd /var/log/packages
ls -la|grep upgraded

showed that several packages were upgraded.

This process completely bypasses the slackpkg system. I suppose I will try slackpkg again sometime, but this alternative works, although downloading all of the Slackware packages seems like overkill.