If you use extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) that can block content (Adblock Plus, NoScript, DuckDuckGo PE, Disconnect, Ghostery, Privacy Badger, uBlock Origin), always make sure such extensions do not block content.

• make sure your extensions and filters are updated to the latest version
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems

You can try these steps in case of issues with webpages:

You can reload webpage(s) and bypass the cache to refresh possibly outdated or corrupted files.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

Clear the Cache and remove the Cookies for websites that cause problems via the "3-bar" Firefox menu button (Settings), click the padlock icon (Clear cookies and site data) for the domain in the selected tab.

"Remove the Cookies" for websites that cause problems:

• Settings -> Privacy & Security
  Cookies and Site Data: "Manage Data"

"Clear the Cache":

• Settings -> Privacy & Security
  Cookies and Site Data -> Clear Data -> [X] Cached Web Content -> Clear

• https://support.mozilla.org/en-US/kb/clear-cookies-and-site-data-firefox
• https://support.mozilla.org/en-US/kb/how-clear-firefox-cache

Start Firefox in Troubleshoot Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration or if userChrome.css/userContent.css is causing the problem.

• switch to the Default System theme: "3-bar" menu button or Tools -> Add-ons -> Themes
• do NOT click "Refresh Firefox" in the Troubleshoot Mode start window

• https://support.mozilla.org/en-US/kb/diagnose-firefox-issues-using-troubleshoot-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems

You can check for issues with Enhanced Tracking Protection. Firefox shows a purple shield instead of a gray shield at the left end of the location/address bar in case Enhanced Tracking Protection is blocking content.

• click the shield icon for more detail and possibly disable the protection

You can check the Web Console for relevant-looking messages like about blocked content.

• https://support.mozilla.org/en-US/kb/enhanced-tracking-protection-firefox-desktop
• https://support.mozilla.org/en-US/kb/total-cookie-protection-and-website-breakage-faq
• https://support.mozilla.org/en-US/kb/trackers-and-scripts-firefox-blocks-enhanced-track

Just in case anyone has the same issue I just had, I'm posting my experience here (since this seems to be an early Google hit for youtube comments issues) and I seem to have fixed the issue *I* was having. I just had a situation where all newly opened Firefox tabs with youtube videos in weren't showing comments. Refreshing misbehaving tabs did nothing. Killing and restarting Firefox did nothing. I then tried in Chrome and had the exact same issue. Turned off my VPN (Malwarebytes), and things started working straight away on both browsers. Turned VPN back on with a different server location and things kept working. Went back to the original server location after a while, and things still work, though I have no idea if they would have worked if I'd gone right back to the original server.