"For what would I use TinyCert certificates? Any place you would use (or should have used) self-signed certificates. Don't leave admin panels, such as phpMyAdmin, a CMS or a webmail install without some protection to keep your password from being intercepted. Use them to protect your test and development installations. Use them on your local POP or IMAP servers. Or use them to test your own code involving certificates." - https://www.tinycert.org/faq#use
I can't control what people do with the certificates, but I'm recommending against the use of TinyCert certificates for the public web. When used as intended, only people who have themselves generated and installed the TinyCert certificates (or their associates if so instructed) will see them and click past. Anybody else should get the big scary warning and will hopefully, rightfully, heed it.
Not being able to trust that you're talking to who you think to are seems like a serious example of "not safe".
Teaching users to click through the warning screen is a serious anti-pattern; the reason browsers keep making it scarier / harder is to try to stop the security theatre that occurs when using untrusted certs.