Are you referring this frontend moderation? http://take.ms/lAXAO

If yes, as long as that is site administrator, they can able to approve/reject for those group/event/page pending request.

I was under the impression that the site administrator could make someone a moderator without making that someone a site administrator in order to let them moderate?

Another option is enable this ACL "Moderate Pending Pages, Events and Groups" from one of your specific profile type, you can refer at my attached screenshot below.

Ahh thank you, I was under the impression that it may be a bit more powerful than that, such as being able to remove posts and ban members etc. Looks like I will need to stick to the old fashioned ways =/

You're most welcome.

Yes, currently only possible to allow moderator to handle that.