Categories are listed in the left margin of that page. You can also use a few (2 or 3) keywords or the name of the add-on in the search area. There are several thousand add-ons; do you really want to search a list that large?

Other issues that need your attention

The information submitted with your question indicates that you have out of date plugins with known security and stability issues that should be updated. To see the plugins submitted with your question, click "More system details..." to the right of your original question post. You can also see your plugins from the Firefox menu, Tools > Add-ons > Plugins.

• Adobe PDF Plug-In For Firefox and Netscape 10.0.0
  • New security update available, version 10.0.1
• Shockwave Flash 10.1 r102
  • New security update available, version 10.2.152.26

1. Check your plugin versions: http://www.mozilla.com/en-US/plugincheck/
   • Note: plugin check page does not have information on all plugin versions
2. Update Adobe Reader (PDF plugin):
   • From within your existing Adobe Reader (if you have it already installed):
     • Open the Adobe Reader program from your Programs list
     • Click Help > Check for Updates
     • Follow the prompts for updating
     • If this method works for you, skip the "Download complete installer" section below and proceed to "After the installation" below
   • Download complete installer (if you do NOT have Adobe Reader installed):
     • Use the links below to avoid getting the troublesome "getplus" Adobe Download Manager and other "extras" you may not want
     • Use Firefox to download and SAVE the installer to your hard drive from the appropriate link below
     • Click "Save to File"; save to your Desktop (so you can find it)
     • After download completes, close Firefox
     • Click the installer you just downloaded and allow the install to continue
       • Note: Vista and Win7 users may need to right-click the installer and choose "Run as Administrator"
     • Download link: ftp://ftp.adobe.com/pub/adobe/reader/
       • Choose your OS
       • Choose the latest #.x version (example 9.x, for version 9)
       • Choose the highest number version listed
         • NOTE: 10.x is the new Adobe Reader X (Windows and Mac only as of this posting)
       • Choose your language
       • Download the file, SAVE it to your hard drive, when complete, close Firefox, click on the installer you just downloaded and let it install.
       • Windows: choose the .exe file; Mac: choose the .dmg file
   • Using either of the links below will force you to install the "getPlus" Adobe Download Manager. Also be sure to uncheck the McAfee Scanner if you do not want the link forcibly installed on your desktop
     • Also see Download link': http://get.adobe.com/reader/otherversions/
     • Also see: https://support.mozilla.com/en-US/kb/Using+the+Adobe+Reader+plugin+with+Firefox (do not use the link on this page for downloading; you may get the troublesome "getplus" Adobe Download Manager (Adobe DLM) and other "extras")
   • After the installation, start Firefox and check your version again.
3. Update the Flash plugin to the latest version.
   • Download and SAVE to your Desktop so you can find the installer later
   • If you do not have the current version, click on the "Player Download Center" link on the "Download and information" or "Download Manual installers" below
   • After download is complete, exit Firefox
   • Click on the installer you just downloaded and install
     • Windows 7 and Vista: may need to right-click the installer and choose "Run as Administrator"
   • Start Firefox and check your version again or test the installation by going back to the download link below
   • Download and information: http://www.adobe.com/software/flash/about/
     • Use Firefox to go to the above site to update the Firefox plugin (will also install plugin for most other browsers; except IE)
     • Use IE to go to the above site to update the IE ActiveX
   • Download Manual installers.
     • http://kb2.adobe.com/cps/191/tn_19166.html#main_ManualInstaller
     • Note separate links for:
       • Plugin for Firefox and most other browsers
       • ActiveX for IE

Just to add to what has already been suggested: you can view all the add-ons this way:

1. If you know partial name or a keyword for the add-on that you are looking for, type it in the search box at top right corner. Otherwise, if you don't want to search for specific keyword, leave the search box empty.
2. Click on the search button.
3. The search results would now be shown. The "Refine Results" column at the left shows all the categories. The search results can now be filtered by selecting the desired category. If you had left the search box empty in step-1, all the add-ons in that category would be listed.

Hope that helps.

Helper7677 obviously did not read my question. 1. "Categories are listed in the of the left margin of that page": I mentioned I select a category in my question, so obviously do not need to have the location of the category list pointed out to me. 2. "You can also use a few (2 or 3) keywords or the name of the add-on": exactly what keywords do I put in? I have spent hours thinking up keywords to get what I want, often ending up using the most unlikely keyword to get the add-in I want; if I knew the name of the add-in already I wouldn't be searching, would I? 3. "There are several thousand add-ins": Yes, but if I selected a category in the old system the number would be filtered to a manageable number - and no, it's no good putting in the category name as a keyword, as there is often no correlation between the category name and the add-in title or description.

No use at all with Firefox 4. If the search box is left empty "Please fill in this field" is returned.

Agreed, there is no easy/direct way to browse through all the add-ons for a category.
In Firefox 4.0, just enter a single space in the search box and click on the search button :)