Make sure you are not blocking content.

Start Firefox in Safe Mode {web link} by holding down the <Shift> (Mac=Options) key, and then starting Firefox.

A small dialog should appear. Click Start In Safe Mode (not Refresh). Is the problem still there?

Separate Issue; Your System Details shows several versions of several programs.
Having more than one version of a program may cause issues. You must remove the older programs. Then get the current full installer.

The site all looks fine for me on Fx59. Probably a separate issue, you have four plug-ins duplicated which need attention. Do you really need all those plug-ins? I recommend that you disable many of them until required. If you haven't already done so you could try the diagnostic Safe Mode. Hold the Shift Key down when you open Firefox. If the images are shown, narrow the plug-ins down - half, quarter etc disabled to track down any problem plug-ins.

Thank you both! I feel really stupid now. It was of course Adblock Plus that was causing the icons to vanish, because I had the "Block social media icons tracking" option enabled! I guess I had probably never used that option before, but when I was setting up the new webextension Adblock Plus version after I upgraded from FF56 to FF58, I thought it was a good idea. The links to Facebook and Twitter are still there though, so I can't really see the point of Adblock Plus just suppressing the icons, but that's a discussion for elsewhere! Thanks again, all is explained! I'm not sure why I apparently have "several versions of several programs". What are they exactly? Also, which plugins are being reported as duplicated? I can't see any problem there. Cheers, Dave.

Hello Dave. The duplicate plug-ins are shown in your Add-ons. To see them on this page look under More System Details>Installed Plug-ins - Duplicates- Adobe PDF Plug-In SVG Viewer DivX Web Player(one in between) Adobe Shockwave for Director I don't know why the alphabetical order is so astray. [We'll see if FredMcD and I overlap again].

Better to overlap than to not know.

Thanks guys! Yes, I've checked the plugins list and there are indeed duplications. They are almost certainly being caused because I have a multi-boot system with three operating systems on it. I have Windows 10, Windows XP, and yes, Windows 98! I guess that Firefox is looking for plugin files over the whole system, not just in the folders of the OS it's running on, and it's finding plugin files in folders that relate to other operating systems that of necessity have different versions of the plugins installed. It's been like that for a long while, and I haven't seen any evidence that it's ever caused any problems. Cheers, Dave.