I have this problem too!

You have asked Firefox to connect securely to blu172.mail.live.com, but we can't confirm that your connection is secure.

Normally, when you try to connect securely, sites will present trusted identification to prove that you are going to the right place. However, this site's identity can't be verified. What Should I Do?

If you usually connect to this site without problems, this error could mean that someone is trying to impersonate the site, and you shouldn't continue.

This site uses HTTP Strict Transport Security (HSTS) to specify that Firefox only connect to it securely. As a result, it is not possible to add an exception for this certificate.

blu172.mail.live.com uses an invalid security certificate.

The certificate is only valid for the following names:

 bing.com, www.bing.com, *.platform.bing.com, *.bing.com, ieonline.microsoft.com, *.windowssearch.com, cn.ieonline.microsoft.com, *.origin.bing.com, *.mm.bing.net, *.api.bing.com, ecn.dev.virtualearth.net, *.cn.bing.net, *.cn.bing.com, *.ssl.bing.com, *.appex.bing.com, *.platform.cn.bing.com, ssl-api.bing.com, ssl-api.bing.net, *.api.bing.net, www.bingsandbox.com, *.bingapis.com, bingsandbox.com, *.working-bingapis-int.com, *.staging-bingapis-int.com, *.working-bingapis-int.net, *.staging-bingapis-int.net  

(Error code: ssl_error_bad_cert_domain)

There is only 1 option " Get me out of here! "

There is nothing Firefox can do about this. You'll need to complain to Microsoft. They'll have to fix their cert.