If you're a domain owner monitoring your own domains, a certificate is suspicious if it was not issued by one of the CAs that you use (e.g. you use Let's Encrypt, but you see a certificate for your domain in CT that was issued by Certinomis). If you keep an inventory of all of your certificates, then you can also cross-reference certificates from CT against your inventory, and flag any certificate that isn't in your inventory.
If you're a security researcher monitoring other people's domains, you have to rely on heuristics - e.g. if a domain has a long history of getting certs from a major US CA, and then suddenly a tiny European CA issues them a certificate, that's pretty suspicious. When I found the example.com certificate misissued by Symantec, I though it was suspicious because it was also valid for subdomains like products.example.com and support.example.com, which don't make sense for a domain that's reserved for documentation purposes. ICANN operates example.com, so I emailed their security team to confirm that they did not authorize the certificate.
The system works best if domain owners are monitoring their own domains, because only they know for sure if a certificate is authorized or not.
In some very prominent countries there are laws with extreme consequences which not only prevent companies from contesting and not complying, but even prevent them ever disclosing such requests.
True, but then they will be found out and distrusted. So basically they'll lose business because of the government of the country they are established in.
