I can see the latest questions on https://money.stackexchange.com/questions?tab=Newest. I can see the latest question or answer activity on https://money.stackexchange.com/questions?tab=Active. But how can I see all the latest comments?
There's no view that displays the most recent comments. However, this information is available through the API, via https://api.stackexchange.com/2.2/comments?order=desc&sort=creation&site=money, even without an app.
If you want a nice, graphical view of it, see fedorqui's answer.
For Meta Stack Overflow, the boson bot has been used to repost all comments to this chat room, which makes it easy to get a view of the most recent comments. I'm pretty sure it can easily be adapted to another site, if you want an archive and not a real-time view (an archive doesn't update on edits or deletions).
The Charcoal team has developed a great tool called Blaze that does exactly this.
If you access https://charcoal-se.org/blaze/#site=money you'll see something like this:
Upon choosing "comments", you'll get the list of comments like this:
As you can see, it allows to auto refresh every certain seconds, so it is a great tool to monitor what is being said in a given site.