SOLVED
Does anyone else have problems with certificates?

Anywhere I check - on my Debian, Ubuntu, OpenSuse systems, Maemo, even Android and iOS... no matter which browser - it's trusted. No idea how my boxes differ from yours in this regard.

If anyone else wants to help, you can try https://neo900.org/ as well - mixed-content warning is expected right now, but the cert itself should be trusted.

My Debian sid has both Certum_Root_CA.pem and Certum_Trusted_Network_CA.pem installed in /etc/ssl/certs

Diagnostic tool for debugging:
openssl s_client -showcerts -CApath /etc/ssl/certs -connect neo900.org:443

(on some systems you may have to fix or ommit -CApath option)

[EDIT]
Disregard this post. I'm stupid. All the time I checked neo900.org, assuming for some reason that it'll work the same cause it's the same cert, while shop subdomain was configured a bit differently. Fixed now, thanks for report!