Certificate Transparency logs are, as explained on the CT site:
simple network services that maintain cryptographically assured,
publicly auditable, append-only records of certificates. Anyone can
submit certificates to a log, although certificate authorities will
likely be the foremost submitters.
The logging of the certificates in this fashion allows for interested parties (e.g. domain owners) to monitor these logs for malicious/erroneous
entries.
But a certificate being logged in a CT log doesn't mean it isn't a bad certificate. As explained on the CT site:
Certificate Transparency relies on existing mitigation mechanisms to
address harmful certificates and CAs--for example, certificate
revocation--the shortened detection time will speed up the overall
mitigation process when harmful certificates or CAs are discovered.
So CT API won't help you in working out whether a certificate is malicious - you need to check using other methods such as checking of certificate revocation lists (CRLs) or by using the Online Certificate Status Protocol (OCSP). See this related question on how to check certs. There are sites that allow for checking of certificates e.g. revocationcheck.com. Modern browsers seem to be converging on the use of compressed lists of CRLs - Mozilla's now using CRLite, whilst Chrome uses CRLSets.
The CT API allows you verify that a certificate has been logged in the CT logs which means that domain owners can monitor them and promptly insert any malicious/erroneous certificates into the relevant CRLs so they won't be used any longer.