That's strange. Does this occur on numerous sites or just on a particular site? For example, this URL should give you an error page:

https://www.sothai.com/ (cert is for the wrong domain)

If you only notice this on particular sites, could you post the URL?

Also, could you test in Firefox's Safe Mode? That's a standard diagnostic tool to deactivate extensions and some advanced features of Firefox. More info: Diagnose Firefox issues using Troubleshoot Mode.

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?

Yes, your example has the same result, including in safe mode. An empty page and a tab titled "Untrusted Connection" with an alert icon.

Firefox has a setting to hide error pages and instead show a pop-up dialog (and if the page was directed to a new tab, a blank page). Are you getting that? If so, you may be able to return to normal by changing the setting here:

(1) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.

(2) In the search box above the list, type or paste xul and pause while the list is filtered

(3) If the browser.xul.error_pages.enabled preference is bolded and "user set" to false, double-click it to restore the default value of true.

If that's not it, perhaps Firefox's program files were damaged in the update. For that, I suggest:

Clean Reinstall

We use this name, but it's not about removing your settings, it's about making sure the program files are clean (no inconsistent, corrupted, or alien code files). As described below, this process does not disturb your existing settings. Do NOT uninstall Firefox, that's not needed.

(1) Download a fresh installer for Firefox 39.0 from https://www.mozilla.org/firefox/all/ to a convenient location. (Scroll down to your preferred language.)

(2) Exit out of Firefox (if applicable).

(3) Rename the program folder, either:

(64-bit Windows folder names)

C:\Program Files (x86)\Mozilla Firefox

to

C:\Program Files (x86)\OldFirefox

(32-bit Windows folder names)

C:\Program Files\Mozilla Firefox

to

C:\Program Files\OldFirefox

(4) Run the installer you downloaded in #1. It should automatically connect to your existing settings.

Any improvement after this reinstall?

Note: Some plugins may exist only in that OldFirefox folder. If something essential is missing, look in these folders:

• \OldFirefox\Plugins
• \OldFirefox\browser\plugins

Yes, a clean reinstall has fixed this. Thank you :)