As in any major upgrade using the package manager to update, for example, from Ubuntu 6.06 to 6.10, there is a danger of something going wrong. It depends on what packages and versions you have installed, if they break dependencies, how you have edited your config files (are they replaced by new stock ones or not, and how that affects the system -- both ways) etc..
Usually the message is: "if you can, do a clean install -- if you can't, use a cd-booted upgrade if available, and only if that is impossible, use package manager update". That's what I recommend: if you had created a separate /home directory when you installed your Ubuntu, you could now just download 6.10 cd, boot from it and install it overwriting the existing installation, but choosing not to format your home partition. That would result in a completely clean update which would work as far as the new distribution version works -- no fear of colliding configuration files or existing packet dependency problems. But usually people just run through their Linux setup and don't create a separate /home directory, and in many cases Linux just creates /home under root, which prevents you from updating the system like I described above.
In this case the next best choice of updating is to boot from the install cd and choose a "upgrade" option from the setup; however I'm not sure if Ubuntu offers that (I haven't checked out the Alternate Install Disc, but I have a feeling Ubuntu does not support this -- Fedora does, for example). So, if you can't back up all your data (for example your complete home directory), do a clean install and then overwrite the existing distribution, nor do you have a separate /home directory (/home in a different partition than root /), then your only choice is -- if you wish to keep your data as safe as possible -- to do an upgrade through apt.
I believe updating trough apt is somewhat safe. By this I mean that it's
probable that either nothing, or only very small things, go wrong. It of course
could be that your system gets trashed, but that's unprobable.
As an example I can mention that a similar upgrade from Fedora Core 4 to 5 could be made using Fedora's package manager
yum, it had similar warnings as you have read, some problems mentioned etc. but I did it on a relatively old Core 4 completely without problems. And even if you had problems, you should be able to fix them, so as long as you don't format anything you are "safe"

you can take a live-cd and burn your data to a safe place any time you like, even if the system died during the upgrade.
Consider what you want; if you don't have a burning need to get some new updates, but you have valuable data that you can't back up (well in that case you should really be able to back it up, so..) or don't want to do such a thing, then keep on using version 6.06. Instead if you are a brave mind, really really want to get the updates and think it's more important than knowing your data is 99,9% safe, just go ahead. I see no reason why you couldn't try. You could run the apt commands first as
dry tests, so that nothing is actually done (i.e. the packages are downloaded, but not installed, the system just "tests to see if it would work"), and if it doesn't produce any big problems, just go ahead and run them the usual way.
If you can't do a clean overwrite-install, go ahead. You're probably just ok, and in case you weren't, borrow your friend's pc and come here and ask how we can fix it up
