Updating from WP 3.3 to 3.6

I developed a site that is currently working with version 3.3. Recently a Facebook Like Button plugin stopped working properly and I feel like it might have to do with the WP version being so out of date. Either way, I’m sure this update needs to happen.

1. Other than exporting the entire content and deactivating the plugins is there anything else I should do before this update?

2. Could there be any issues with this update? I am worried that it will somehow change the appearance of the site that currently looks great (other than the FB button issue).

Thank you!