Database integrity ?

Good day everyone.

I am posting this question on the mailing list even though
I am also trying to research it as all information will be helpful.

Our client are currently running about 13 servers with
100 odd databases spread across these servers.

One of my most important tasks to look at, at the
moment, is to look at the data integrity of their databases as it seems
that some information are being duplicated unneccesarily and it might
also be possible that data integrity have been compromised due to this.

I was just tasked to look into the data integrity,
however, as I am still a postgres newbie I am not even sure where to
begin considering the amount of databases. Some of these databases have
over a thousand tables in them.

Does anybody perhaps have some experience on this
front in order to provide me with some tips or advice as I would really
appreciate it?

Regards
Machiel