I'm a total Linux newb with an installation of Slackware 10.2, kernel release 2.4.31 on a Sony VAIO laptop. So far so good. A lot of things are working, though I'm sure a lot of things are not working as they should.

When I boot, a lot of text scrolls by quickly on the screen, with occasional pauses. Not all of the messages are favourable: this or that failed to load, something loaded in read-only mode, but it all scrolls by too quickly to make a note. Is there a way to capture this boot text so that I can use it diagnostically? Or is there another systematic way to identify these problems?

Thanks for your help.

You can use less or more, I like less.
from a terminal as root;
dmesg | less

dmesg will not show you all the stuff that scrolls by at boot. I do not know specifically about you distro, but for Debian I simply edited the file /etc/default/bootlogd and added the line "BOOTLOGD_ENABLE=Yes". After booting, I can then find all the boot messages in the file /var/log/boot

Also, in general it's OK for a few things to fail at boot time (e.g. probes of hardware you don't have). Usually what I do is look for things that aren't working and then go back to the boot messages and try to figure out why. The dmesg command mentioned above shows output from the kernel. If the failures occur after init (the first process that is responsible for starting all the other processes) and are caused by non-kernel programs, you'll need something like bootlogd. I don't have that installed by default on my Slack 10.2 system so you may need to go download it from linux-packages.net or build it from source and then add a line starting it in /etc/rc.d/rc.S (probably towards the beginning) as this script is executed towards the beginning of things.