I just got the Java update to Version 7 Update 10 after reading this discussion, even though I just installed Version 7 Update 9 two days ago. But, I thought I'd test this on my laptop running Windows Vista and Firefox 17.0.1 since you have the same OS and version of Firefox.
Just before updating, I opened Firefox and went to
http://www.java.com/en/download/installed.jsp and clicked the button for
Verify Java version. It confirmed I had Java Version 7 Update 9. To get the update to version 10, I opened the Java control panel from Windows Control Panel and initiated the update. I then opened Firefox and went to
http://www.java.com/en/download/installed.jsp and clicked the button for
Verify Java version again to verify. This time, it simply would not confirm that I had Java installed. I clicked on Tools (on Firefox menu) and selected Add-ons. Next, I selected Plugins on the left column since it was not already selected when I opened the Add-ons panel. I saw that the Java plugin was disabled. So, apparently, Firefox or Java disabled the plugin during installation of Java Version 7 Update 10. I enabled the plugin, closed Firefox, reopened it, went again to
http://www.java.com/en/download/installed.jsp and clicked the button for Verify Java version. This time, the verifcation procedure confirmed Java was working in Firefox.
However, I'm going to disable it since, like other forum members have said, I rarely encounter a website that uses it. Also, the Firefox panel for plugins shows a warning in small gold text above the Java plugin; it says "Java (TM) Platform SE 7 U5 is know to cause security or reliability issues." Next to this text is a link title "More information". It leads to
https://addons.mozilla.org/en-US/firefox/blocked/p134. That link refers to update versions 6 and below, so I'm not sure why it would be displayed in connection with later update versions.