Drupal 5.8 and 6.3 fix security issues
I upgraded three 6.2 sites and one 5.7 site, went very smoothly
I "cheated" the upgrade:
I did not switch the theme, or disable contributed modules, or delete the old code (I just wrote the new files over the old) as suggested in the Upgrade instructions, and I had no problems
of course, make sure you back up b4 upgrading!