Consumers and publishers take certificates and certs for granted. I see many broken certs, or brands using the wrong certs and domains for their services.
SSL/TLS has done well to prevent eavesdropping, but it hasn't done well to establish trust and identity.
At the same time, it sounds like the issues you describe aren’t CA/issuance issues, but rather, simple misconfigurations. Those aren’t incidents for the ecosystem, although definitely can be disruptive to the site, but I also wouldn’t expect them to call trust or identity into disrepute. That’d be like arguing my drivers license is invalid if I handed you my passport; giving you the wrong doc doesn’t invalidate the claims of either, just doesn’t address your need.
There is systematic checking - e.g. crt.sh continuously runs linters on certificates found in CT logs, I continuously monitor domains which are likely to be used in test certificates (e.g. https://bugzilla.mozilla.org/show_bug.cgi?id=1496088), and it appears the Chrome root program has started doing some continuous compliance monitoring based on CT as well.
But there is certainly a lot of ad-hoc checking by community members and academics, which as Sleevi said is one of the great things that CT enables.