I've noticed that this week we're getting a lot of tiny pointless edits to posts (https://serverfault.com/users/100013/jakegould, https://serverfault.com/users/294235/lnux?tab=activity) - how are they getting approved and should we do something about it?
Should we do something about these minor edits?
Tiny, trivial edits are discouraged and should be rejected when you encounter them in the review queue.
Although it is a good thing to edit and improve incorrect and outdated content the main disadvantage is that even a minor edit (on an older Q&A) bumps it to front page. So make your edits count on those posts.
On newly posted Q&A's; if you feel you can make the post better, and are inclined to do so, please edit!
How are they getting approved?
It only takes a minimal amount of rep before a user is allowed to propose edits to Q&A's, but those are not applied automatically. They enter a review queue where they need to be approved by 2 established users (= rep > 2000) or a moderator. Those same users can see the audit trail and the review history here: https://serverfault.com/review/suggested-edits/history
Maybe the original author of the question/answer can also allow edits outside of the review queue, I'm not sure.
Established users (= rep > 2000) get the privilege to have their edits applied immediately, without peer review.
The user you linked to: https://serverfault.com/users/100013/jakegould?tab=activity
Is one such established users (= rep > 2000) who has achieved both the privilege to have their edits applied immediately, without peer review and the privilege to participate in the edit review queue.
The edit you linked to here: https://serverfault.com/users/294235/lnux?tab=activity
Was by a low-rep user and got approved from the review queue here by a fellow moderator.