If you're just using lucid-updates, the policies are pretty solid for stable release updates. Basically only small changes that won't change the behavior of the software in an incompatible way are allowed.
Here are some steps you can take to make sure it goes smoothly.
1) Read the change logs for all new packages. If you're using apt-get upgrade, look at the list of packages that are going to be updated. The easiest way is to use aptitude (apt-get install aptitude if you don't already have it):
aptitude changelog foo
This will show you the changelog of the package, including un-applied updates. If you see something like "LP: #123456" this is a Launchpad bug report that has been fixed by that update, you can read the full bug report at http://launchpad.net/bugs/123456
2) backup our system. You should be doing this anwyay!
3) Schedule downtime. While most updates won't cause LONG downtime, they will probably involve restarting services to pickup updated configurations and/or libraries, so be ready to have brief service interruption.
3a) Test stopping/starting your services BEFORE the update. We get a lot of bug reports in Ubuntu from users thinking an update broke their system, when in fact the configs had been wrong for a while but the problems had gone unnoticed because the service was running fine with the old, non-broken configuration.