The current release's (188.8.131.52.21) Check for Updates, even if it connects properly, does not include Third Party JDBC drivers in any of the update center lists. For that, you are better off finding the jtds driver on the web, then install it via
Tools > Preferences > Database > Third Party JDBC Drivers > Add Entry...
To use jtds-1.3.0.jar, your SQL Developer release must point to Java 7 (jdk1.7.0_xx) or higher. The jtds-1.2.0.jar, the certified version according to the Oracle documentation, works with Java 6 (jdk1.6.0_xx) but also works with Java 7 as far as I know.
Now, back to Check for Updates. If Test Proxy succeeds but the Unable to Connect dialog keeps popping up, that is likely due to the Unable to refresh list of update centers warning in the Check for Updates wizard. Maybe a server is down. If you do not wish to wait for the server to come back up, just cancel out of the Unable to Connect dialog and click the Next button in the Check for Updates wizard. If nothing is available in the Search Update Centers area in Step 1 of 4, you can try the following URLs in your web browser, then look for the bundle-url of the specific update you wish to dowload, download it, then use the Install From Local File option to install it:
Oracle SQL Developer: http://apex.oracle.com/pls/apex/dbtools/usage/cfu
Third Party SQL Developer Extensions: http://www.oracle.com/ocom/groups/public/@otn/documents/webcontent/162033.xml
SQL Developer Team
I believe I have the latest release, but the 'Next' button is disabled after I cancel the proxy setup/test dialog. The 'Test Proxy' does succeed.
oracle.ide.webbrowser.HttpPing$PingFailedException: Unable to connect
The list of 'Update Centers' is currently empty, btw.
Is there 1 I can manually add?
Yes, just use the names and links provided in my prior post. Click on the Add... button to the right of the Search Update Centers section of the Check for Updates wizard page Step 1 of 4.
I believe the Oracle Extensions center currently has nothing available, so if checking that off somehow prevents display of content in the other centers, just un-check its box.