Apple’s big iOS update, iOS 6, is hitting iPhones, iPads and iPod Touches today, but Mac OS X Mountain Lion is also getting an update with version 10.8.2.

New Facebook integration is a major component of iOS 6, and now Mac OS X is stepping up the integration as well.

Among the new features of the operating system are single sign on for Facebook, the addition of Facebook as an option when sharing links and photos, seeing Facebook friends’ contact info and profile pics in Contacts, and Facebook notifications in Notification Center.

In Game Center, you can now share scores to Facebook, Twitter, Mail, or Messages, Facebook friends are included in friend recommendations, Facebook “like” buttons have been added for games, and friends can be challenged to beat your scores and achievements.

Apple is really doing everything in its power to get people sharing on Facebook even more.

In addition to the Facebook and Game Center stuff, Apple has added the following features:

• Adds Power Nap support for MacBook Air (Late 2010)
• iMessages sent to your phone number now appear in Messages on your Mac*
• You can now add passes to Passbook (on your iPhone or iPod touch) from Safari and Mail on your Mac*
• FaceTime can now receive calls sent to your phone number*
• New shared Reminders lists
• New sort options allow you to sort notes by title, the date you edited them, and when you created them
• Dictation now supports additional languages: Mandarin, Cantonese, Spanish, Korean, Canadian English, Canadian French, and Italian
• Dictionary app now includes a French definition dictionary
• Sina Weibo profile photos can now be added to Contacts

* Requires iOS 6

The update also comes with some general fixes:

• Adds an option to discard the changes in the original document when choosing Save As
• Unsent drafts are now opened automatically when launching Mail
• Receive Twitter notifications for mentions and replies from anyone
• URLs are shortened when sending tweets from Notification Center
• Notifications are disabled when AirPlay Mirroring is being used
• Adds SSL support for Google searches from the Smart Search Field in Safari
• Adds a new preference to have Safari launch with previously open webpages
• Resolves an issue that may cause the “Enable Autodiscover” checkbox to always remain checked
• Enables access to the Mac App Store when Parental Controls are enabled
• Support for @icloud.com email addresses
• Resolves a video issue with some VGA projectors when connected to certain Mac notebooks
• Addresses an issue that may prevent Active Directory accounts from being locked out
• Resolves an issue that may cause the policy banner to re-appear prior to logging in
• Improvements to SMB
• Addresses an issue with NIS users when auto-login is enabled
• Addresses an issue in which the Keychain may not be accessible
• Ability to pre-authenticate a FileVault protected system
• Addresses an issue that may cause Xsan to not automatically start after migrating from Mac OS X Snow Leopard