I have disabled Sociable and installed a similar social bookmarking plugin. All issues are now resolved. I most likely will not be testing this any further.

If I get the opportunity to try all of the plugins in a testing environment, I will let you know what I find.

Sorry, copy-paste method doesn't look so great. It's actually the latest version:

Select Sociable    Sociable
Deactivate | Edit
   

Automatically add links on your posts, pages and RSS feed to your favorite social bookmarking sites.
Version 4.2.6 | By Blogplay | Visit plugin site

Disabling all plugins on a live site is out, but I can do one by one for a few seconds. I guess the combination of Sociable AND another plugin could be causing the issue.

This is a full list of the plugins the site is using (some not activated). I've ***'d out private data.

Select Add From Server    Add From Server
Import Files | Options | Deactivate | Edit
   

Plugin to allow the Media Manager to add files from the webservers filesystem. Note: All files are copied to the uploads directory.
Version 3.2.0.2 | By Dion Hulse | Visit plugin site
Select Akismet    Akismet
Activate | Edit | Delete
   

Used by millions, Akismet is quite possibly the best way in the world to protect your blog from comment and trackback spam. It keeps your site protected from spam even while you sleep. To get started: 1) Click the "Activate" link to the left of this description, 2) Sign up for an Akismet API key, and 3) Go to your Akismet configuration page, and save your API key.
Version 2.5.3 | By Automattic | Visit plugin site
There is a new version of Akismet available. View version 2.5.5 details or update automatically.
Select All in One SEO Pack    All in One SEO Pack
Activate | Edit | Delete
   

Out-of-the-box SEO for your Wordpress blog. Options configuration panel | Upgrade to Pro Version | Donate | Support | Amazon Wishlist
Version 1.6.13.4 | By Michael Torbert | Visit plugin site
There is a new version of All in One SEO Pack available. View version 1.6.13.8 details or update automatically.
Select *** Banners    *** Banners
Activate | Edit | Delete
   

Simple Banner Rotation Program for *** Theme of WP
Version 1.0 | By *** | Visit plugin site
Select Constant Contact API    Constant Contact API
Activate | Edit | Delete
   

Powerfully integrates Constant Contact into your WordPress website.
Version 2.3.1 | By Katz Web Services, Inc. & James Benson | Visit plugin site
There is a new version of Constant Contact API available. View version 2.3.6 details or update automatically.
Select Constant Contact API: Form Designer (Alpha)    Constant Contact API: Form Designer (Alpha)
Activate | Edit | Delete
   

Create fancy-lookin' forms for the Constant Contact API plugin that have tons of neat configuration options.
Version 2.3.1 | By Katz Web Services, Inc. | Visit plugin site
There is a new version of Constant Contact API: Form Designer (Alpha) available. View version 2.3.6 details or update automatically.
Select Contact Form 7    Contact Form 7
Settings | Deactivate | Edit
   

Just another contact form plugin. Simple but flexible.
Version 3.0 | By Takayuki Miyoshi | Visit plugin site
There is a new version of Contact Form 7 available. View version 3.1.1 details or update automatically.
Select Contact Form to DB Extension    Contact Form to DB Extension
Deactivate | Edit
   

Save form submissions to the database from Contact Form 7 and Fast Secure Contact Form. Includes exports and short codes. | Data | Settings | FAQ
Version 2.1 | By Michael Simpson | Visit plugin site
There is a new version of Contact Form to DB Extension available. View version 2.3 details or update automatically.
Select Dagon Design Sitemap Generator    Dagon Design Sitemap Generator
Deactivate | Edit
   

Generates a fully customizable sitemap
Version 3.15 | By Dagon Design | Visit plugin site
Select Downloads Manager    Downloads Manager
Deactivate | Edit
   

This Plugin adds a simple downloads manager to your blog.
Version 1.0 rc-1 | By Giulio Ganci | Visit plugin site
Select FancyBox for WordPress    FancyBox for WordPress
Activate | Edit | Delete
   

Integrates FancyBox by Janis Skarnelis into WordPress.
Version 2.7.5 | By José Pardilla | Visit plugin site
There is a new version of FancyBox for WordPress available. View version 3.0.1 details or update automatically.
Select Flexi Quote Rotator    Flexi Quote Rotator
Activate | Edit | Delete
   

Based on Luke Howell's quote rotator, the flexi quote rotator allows you to add the quotes to your site using a shortcode or php snippet in template instead of only as a widget. Also adds flexibility with styling and setting durations.
Version 0.3.2 | By Aidan Curran | Visit plugin site
Select Google Analytics for WordPress    Google Analytics for WordPress
Settings | Deactivate | Edit
   

This plugin makes it simple to add Google Analytics to your WordPress blog, adding lots of features, eg. custom variables and automatic clickout and download tracking.
Version 4.1.3 | By Joost de Valk | Visit plugin site
There is a new version of Google Analytics for WordPress available. View version 4.2.4 details or update automatically.
Select Google Calendar Events    Google Calendar Events
Settings | Deactivate | Edit
   

Parses Google Calendar feeds and displays the events as a calendar grid or list on a page, post or widget.
Version 0.7.1 | By Ross Hanney | Visit plugin site
There is a new version of Google Calendar Events available. View version 0.7.2 details or update automatically.
Select Google XML Sitemaps    Google XML Sitemaps
Deactivate | Edit
   

This plugin will generate a special XML sitemap which will help search engines like Google, Yahoo, Bing and Ask.com to better index your blog.
Version 3.2.6 | By Arne Brachhold | Visit plugin site | Settings | FAQ | Support | Donate
Select Hello Dolly    Hello Dolly
Activate | Edit | Delete
   

This is not just a plugin, it symbolizes the hope and enthusiasm of an entire generation summed up in two words sung most famously by Louis Armstrong: Hello, Dolly. When activated you will randomly see a lyric from Hello, Dolly in the upper right of your admin screen on every page.
Version 1.6 | By Matt Mullenweg | Visit plugin site
Select Links Shortcode    Links Shortcode
Deactivate | Edit
   

Displays all links of a certain category in a post using a shortcode, according to a definable template. Includes optional Facebook Like button.
Version 1.0 | By Maarten Swemmer | Visit plugin site
There is a new version of Links Shortcode available. View version 1.1 details or update automatically.
Select Multi Sliding Banner    Multi Sliding Banner
Deactivate | Edit
   

A Multi Sliding Banner for WordPress
Version 1.8.3 | By *** | Overview
Select Random Text    Random Text
Deactivate | Edit
   

A widget to display randomized text on your site
Version 0.2.8 | By Greg Jackson | Visit plugin site
There is a new version of Random Text available. View version 0.2.9 details or update automatically.
Select Redirection    Redirection
Settings | Deactivate | Edit
   

Manage all your 301 redirects and monitor 404 errors
Version 2.2.9 | By John Godley | Visit plugin site
There is a new version of Redirection available. View version 2.2.10 details or update automatically.
Select Search & Replace    Search & Replace
Settings | Deactivate | Edit
   

A simple search for find strings in your database and replace the string.
Version 2.6.2 | By Frank Bültge | Visit plugin site
There is a new version of Search & Replace available. View version 2.6.3 details or update automatically.
Select Shadowbox JS    Shadowbox JS
Settings | Deactivate | Edit
   

A javascript media viewer similar to Lightbox and Thickbox. Supports all types of media, not just images.
Version 3.0.3.8 | By Matt Martz | Visit plugin site
Select Shadowbox JS - Use Title from Image    Shadowbox JS - Use Title from Image
Deactivate | Edit
   

Push the title attribute from the img tag to the anchor tag
Version 3.0.3.8 | By Matt Martz | Visit plugin site
Select Sociable    Sociable
Deactivate | Edit
   

Automatically add links on your posts, pages and RSS feed to your favorite social bookmarking sites.
Version 4.2.6 | By Blogplay | Visit plugin site
Select Square Thumbnails for User Photo    Square Thumbnails for User Photo
Deactivate | Edit
   

Extends the User Photo plugin to allow the generation of square thumbnails. (Requires the User Photo plugin, WILL NOT WORK otherwise.)
Version 1.2.1 | By Simon Wheatley | Visit plugin site
Select Stray Random Quotes    Stray Random Quotes
Activate | Edit | Delete
   

Display and rotate random quotes and words everywhere on your blog. Easy to custom and manage. Ajax enabled.
Version 1.9.9 | By unalignedcoder | Visit plugin site
Select Theme My Login    Theme My Login
Deactivate | Edit
   

Themes the WordPress login, registration and forgot password pages according to your theme.
Version 6.1.4 | By Jeff Farthing | Visit plugin site
Select Theme Preview    Theme Preview
Activate | Edit | Delete
   

Allows themes to be previewed without activation
Version 1.2 | By Dougal Campbell | Visit plugin site
Select User Photo    User Photo
Deactivate | Edit
   

Allows users to associate photos with their accounts by accessing their "Your Profile" page. Uploaded images are resized to fit the dimensions specified on the options page; a thumbnail image is also generated. New template tags introduced are: userphoto_the_author_photo, userphoto_the_author_thumbnail, userphoto_comment_author_photo, and userphoto_comment_author_thumbnail. Uploaded images may be moderated by administrators.
Version 0.9.5.1 | By Weston Ruter | Visit plugin site
Select WP-Cufón    WP-Cufón
Deactivate | Edit
   

Enables Cufón font-replacement in WordPress - After installation you only have to put your generated font-files to /wp-content/plugins/fonts/ directory. Go to the Settings Page for more instructions and to add your own replacement scripts.
Version 1.6.10 | By Tobias Battenberg | Visit plugin site
Select WP-SimpleViewer    WP-SimpleViewer
Deactivate | Edit
   

Create SimpleViewer galleries with WordPress.
Version 2.3.0 | By SimpleViewer Inc. | Visit plugin site
Select WP Easy Uploader    WP Easy Uploader
Deactivate | Edit
   

Easily upload any type of content without the need for FTP. You can even upload plugin and theme archives and have the files automatically extract into the plugin or theme folder.
Version 1.0.11 | By Chris Jean | Visit plugin site

Steven Speirs wrote:

@YaegerDesign

I have just installed and activated Sociable v4.2.6 to test and have successfully been able to create a gallery with WP-SimpleViewer v2.3.0 (and previously created galleries also still work OK). The 'Add Gallery' button seems to function fine with Sociable the plugin installed.
Do you have any other plugins (or are you using a non-default theme) which may be causing the conflict you are experiencing?

I tried disabling multiple plugins (which use jQuery). When I disabled the Sociable plugin, everything worked fine. The site is using a custom-built theme. However, that shouldn't matter in the admin side. I suspect that Sociable's option additions to the post/page creator in the admin are what caused the conflict. I could tell that jQuery wasn't running in the SimpleViewer window because choosing "Wordpress Library" didn't hide the Flickr fields.

The "Sociable" plugin is causing the same conflict...
http://wordpress.org/extend/plugins/sociable/