This is from memory, so bear with me...

For AIX server 3.7.x to 4.1 upgrades:
Check OS patch levels against required levels in the release/patch README
Check device driver levels against the required levels in the release/patch
README
Make sure your copystgpools are current.
Do a BACKUP DB type=full

Down TSM server process and stop all instances of dsmadmc, dsmcad, dsmc, dsm
and dsmserv

For the truly paranoid:
Create a fresh mksysb
Create backup copies of the following files in /usr/tivoli/tsm/server/bin
device config file
volume history file
dsmserv.dsk
dsmserv.opt

Mount 4.1 installation media, install using smitty (The README has the
appropriate options to use).

Verify startup scripts -
(If you use some variations of externally managed libraries, the startup
sequence may need to be changed from 3.x to 4.x due to some timing issues at
startup - though if it works, don't break it ;))

Reboot the AIX box so the bosboot changes will be in effect. (this may not
be strictly required, but it gives me warm fuzzies..)

Don't be alarmed if the TSM startup time is slightly longer on the first
startup - an UPGRADEDB is automagically run.

Once the TSM server has started, log in and verify your configuration.

Repeat the above steps as your paranoia dictates for the next patch/release
level you desire...

The licensing issue with 4.1, if I remember correctly, was that certain
levels of the 4.1
release would not allow you to re-use a license file - TSM ships with a 1,
5, 10 and 50 count license file for various things - 10mgsyslan.lic is the
10 license file for managed LAN nodes.  In those levels of 4.1, you could
only have 66 licenses active without some sort of magic.  Everything still
worked, you just got these annoying messages in the activity log constantly.
This issue was fixed in 4.1.5.0 I believe, maybe earlier.

I'm sure I left several critical steps out, everyone jump right in and
correct me please...