By default, Firefox checks secure websites for authentication in the form of a security certificate, and prevents you from accessing those whose certificate is either self-signed, forged or expired. Since an "Untrusted Connection" warning doesn't necessarily indicate malicious intent, you can opt to bypass the security warning if you know you can trust the website. Completely disabling the "Untrusted Connection" warning in Firefox, however, may leave your computer vulnerable to attack. Use the Exceptions feature in Firefox to allow only websites of your choosing to bypass the warning screen.
Add a Website to Firefox Exceptions List
When you try to access a trusted website and Firefox presents you with the "This Connection is Untrusted" warning, click the "I Understand the Risks" option. On the following screen, click "Add Exception" to bring up the Add Security Exception dialog box. Click "Confirm Security Exception" to add the website to the Firefox Exceptions list. You can now directly visit the website without the "Connection Untrusted" screen popping up.
Skip Cert Error Add-on
Rather than individually adding exceptions to multiple websites, you can use the Skip Cert Error add-on (link in Resources) for Firefox. It lets you skip the "Connection Untrusted" screen for secure websites that have self-signed or otherwise invalid security certificates or mismatched domain names. On the download page, click the "+ Add to Firefox" button, then click the "Restart Now" button to complete the add-on installation. Navigate to the Firefox add-on screen by pressing "Ctrl-Shift-A," then click the "Extensions" side-tab. Click the "Options" button next to Skip Cert Error, check the box next to "Enable Bypass," then click "OK" to finalize the changes.