I'm talking about the old tools links; I hope they will be staying.
I find numerous posts this way that have slipped through the 'Review' system due to people simply gaming it. For example, I just finished flagging a bunch of a series of spam posts by a handful of users - each person's first post was up-voted a couple times, almost certainly due to the "First Posts" review queue.
Beyond this, there are still occasions where people are simply mis-Reviewing, in my opinion. The more 'raw' views of the Tools menu gives those of us who are interested a way to dig through things to, well... review the reviewers, or sometimes catch things that don't end up in the Review queues anyway. (For instance; the late answers to old posts "Tools" item shows all late answers - not just those from 'new' users - and I frequently catch spammy answers there.
EDIT: A clarification; I guess I'm also most specifically talking about the aforementioned New Answers to Old Questions item