However, if there are many non-default modules you're using, there might be some tricky things. Here's what I ran into:
Problem #1: Forum Access problems:
This error was shown after submitting a new forum entry:
Solution:Fatal error: Call to undefined function acl_node_add_acl() in /home/user/install/drupal-5.20/modules/forum_access/forum_access.module on line 379
I forgot to copy the "acl" module, so it was missing in the new installation.
Problem #2: Gallery2 integration
When opening the embedded Gallery2 in my Drupal, I saw the main albums, but clicking on any one of them returned a "page not found" error. Browsing the gallery directly (not through Drupal) worked great.
Solution:
The ".htaccess" file in the Drupal directory was missing the URL-rewrite entries that the gallery2-module for Drupal adds during its installation. I've just copy/pasted it from the old .htaccess to the new one.
Problem #3: Gallery2 Theme broken
Before the update, the embedded gallery was using the "matrix" (=default) theme from Gallery2. After the upgrade however the design was displayed broken in the browser.
Solution:
I forgot to make the "gallery2" symlink in the Drupal directory, pointing to the Gallery2 installation folder (in my case: drupal/gallery2 -> ../gallery2)