The best way to avoid such phobia is to:
A) Backup all site files and your database (full site backup)
B) Deactivate all plugins.
C) Switch to default twentyeleven theme.
D) Run Auto-Update.
E) Run site to make sure it runs in default setup.
F) Once site is at 3.4.1, you will be notified of any necessary updates at admin screen.
G) If your theme needs an update, and you have customized your theme, you WILL lose those on a theme update. Look at Child Themes. Activate theme after the update.
H) If a plugin needs an update, update if before you re-activate it. Activate plugins one at a time, run site, to test each plugin.
And finally, nothing in this fair world is perfect, if you encounter an issue, you can restore your site with the backups <=most important step is A.
