Yes, many of the problems from CT are fixed. I wouldn't call it a "broken mess" though, as it has been relatively effective at detecting various problems, and to my knowledge hasn't been compromised.

There are no SCTs, which were a compromise to get CT shipped. Each Merkle Tree Certificate has an actual inclusion proof in it.

CT has multiple independent logs, and requires certs to be logged to 2+ of them. With MTC, you have one issuing log, along with signatures from other "witnesses" which monitor and mirror log integrity. Those co-signatures are validated when checking the certificate.

Thus the witness network makes it much harder for logs to fork, as you can't present a forked view to just the client. You also need to present it to a witness. And it'll be much easier for folks to check all the witnesses are in sync.

Monitoring the MTC logs will be easier than CT, as they'll actually be smaller than CT for a few reasons. At least for the initial version, there won't be a better way to monitor for mis-issued certificates for a particular domain than linear scanning all certificates, but that's a problem being worked on for both CT and MTC, called "verifiable indexes".