Be careful to downgrade WordPress unless you can also restore a pre-upgrade database backup. The database was changed for WordPress 3.6
If you are facing issue with plugins deactivating all plugins and re-activate one by one again.
Change your theme to default one for a while to check your issues is solved.
If you are still on decision to downgrade wordpress go through following steps.
1. Login to your wordpress Dashboard.
2. After you login to the WordPress. Goto plugins and deactivate all the plugins.
3. Login use FTP of your site either via FTP client or from cpanel. locate your wordpress root directory which has wp-admin and wp-includes folder.
4. For precaution download entire site from root directory.
5. Delete all files and folder other than wp-content. just leave wp-content folder as it is.
6. Download wordpress version you want to downgrade/Upgrade from wordpress.org and extract it in local and Copy all the WordPress files and folders to your server.
7. in case of wp-content it’ll ask for overwrite say yes if file size or source is different.
8. Now Login to your WordPress Dashboard. You will get following message. Click on “Update WordPress Database”.
9. On finish setup it’ll ask to continue. Click on “continue” to login to your Dashboard.
10. You have now successfully downgraded wordpress. Once you login to your dashboard you can see the wordpress current version.