Do you mean that additional CSS files are blocked?

You can check the log in the Web Console for error messages and the Network Monitor (Firefox/Tools > Web Developer) to see if content fails to load or is possibly blocked.

• https://developer.mozilla.org/Tools/Web_Console
• https://developer.mozilla.org/Tools/Network_Monitor

Use Ctrl+F5 or Ctrl+Shift+R to reload the page and bypass the cache to generate a fresh log.

You can reload web page(s) and bypass the cache to refresh possibly outdated or corrupted files.

• Hold down the Shift key and left-click the Reload button
• Press "Ctrl + F5" or press "Ctrl + Shift + R" (Windows,Linux)
• Press "Command + Shift + R" (Mac)

I tried to interpret the results in the console - but could find no differences. The 2 web pages are

http://www.162smilingfaces.com/Esther_Lewis.html and 

http://162smilingfaces.com/Esther_Lewis.html . The first doesn't show the image of the lady, the second does. This issue is not limited to this page but is on all pages in the site and suppresses different elements (not text). [Again, not an issue on other browsers.]

I'm not seeing any difference between the two pages and the Network log shows the same remote address (IP) for both pages.

Did you you check the Network log?

Do you see the images in "Tools > Page Info > Media"?

Can you load missing images via the location/address bar?

Could you completely clear Firefox's Cache. The cache contains temporary copies of pages and images and doesn't remove history. During development you may occasionally get old versions "stuck" in the cache and not updating. See: How to clear the Firefox cache.

You might also want to test in Firefox's Safe Mode. In Safe Mode, Firefox temporarily deactivates extensions, hardware acceleration, and some other advanced features to help you assess whether these are causing the problem.

If Firefox is not running: Hold down the Shift key when starting Firefox.

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" button > Restart with Add-ons Disabled
• Help menu > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Any improvement? (More info: Diagnose Firefox issues using Troubleshoot Mode)

You can remove all data stored in Firefox from a specific domain via "Forget About This Site" in the right-click context menu of an history entry ("History > Show All History" or "View > Sidebar > History") or via the about:permissions page.

Using "Forget About This Site" will remove all data stored in Firefox from that domain like bookmarks, cookies, passwords, cache, history, and exceptions, so be cautious. If you have a password or other data from that domain that you do not want to lose then make sure to backup this data or make a note.

You can't recover from this 'forget' unless you have a backup of the involved files.

If you revisit a 'forgotten' website then data from that website will be saved once again.

Thanks to Cor-el.

"Do you see the images in "Tools > Page Info > Media"?" ...

In this dialog, I noticed that the check box for "Block Images from ..." was checked when a leading www was in the URL but unckecked when there was no www. How it got checked is beyond me. Thanks for the path which provided the solution and to the others who offered their solutions.