Chrome itself does not act as a monitor, that is left to domain owners. CT guarantees detectability, but only if someone's looking.
CT also has a gossip protocol that should help detect misbehaving log servers; I'm not too familiar with that protocol and whether Chrome has implemented any of it. That's an area where I guess there might be some privacy concerns to think about.
The fundamental idea is to make all certificate creation public, by putting it in a publicly auditable list. THis allows anyone to check that someone else hasn't given out a certificate for their domain, or for a large chunk of the internet etc.
In order to make that work, you have to make all certificates that aren't in that list unusable, and you do that by having the browser check that the certificate it is checking is in the list.
I suppose a client could act more like a monitor and download chunks of the log at a time, thereby hiding which site in the chunk they were interested in. That wouldn't be hugely efficient though.
Auditors and CT gossiping are responsible for ensuring that the log servers are not misbehaving.