I'm not sure what the issue is, but for some reason the WP Thickbox Integration Plugin (http://wordpress.org/extend/plugins/wp-thickbox-integration/) does not play nicely with Advanced Custom Fields (http://wordpress.org/extend/plugins/advanced-custom-fields/).
If I setup an Image field in ACF, while the WP Thickbox Integration plugin is enabled, whenever I click "Select Image" in the admin panel, it doesn't actually select the image. Once I disable the thickbox plugin, everything works properly with ACF again.
I can build the thickbox functionality directly into my theme, so I've disabled the thickbox plugin in favor of ACF. Not sure which plugin is actually causing the problem though.