All of the edits in that list were approved by some users but rejected by others. It looks like what makes them controversial is that at least one user disagreed with the decision taken by others.
You can see this by clicking on the "approved" link which takes you to the page of the edit suggestion.
The /tools link was removed some time ago (that screenshot is from Jan '12) , and /review is there in its place.
The whole point of the feature is to make it easier for mods/editors to find stuff that might be worth checking out, and /review is more efficient at that, so it gets a prime spot at the top.
People have the privilege if deleting in order to be able to remove posts that need to be deleted. This is a quasi-moderation privilege so treat it with the same respect we do.
If we're talking about questions, the close system should be used first. This allows a poster to revise and reopen their question. And closing it without answers or positive score ...
Reviewing flags is mostly a privilege gained by winning a moderator election – and not by reputation. There once was a flag queue for 10 k users but it was abolished a few years ago.
The only exceptions are:
not-an-answer and very-low-quality flags, which send posts to the low-quality queue, where you can review with 2 k reputation;
close flags, which send ...
It was rolled up into the standard review process. Here's part of Shog9's answer:
/tools/flagged is no more. Disputed flags are still a thing, but disputes are situations observed by the system, not explicit actions. The guidance for new 10K users has been revised: https://stackoverflow.com/help/privileges/moderator-tools
Since you are copying the meta SO thread here, we should also include the (very) important exception to the guidelines you cite. This is a screenshot, taken on March 16th, 2014 of the second highest voted answer from the same Q&A:
So, follow the rules above in general but avoid deleting questions closed as duplicates because they are useful "guideposts"....
First, I recommend checking to make sure you can open up the post. Maybe it's been deleted already and is just sticking around in the flag queue for a short time. If that's the case, and it disappears from the 10k tools soon, then you don't have to do anything.
If the post still exists, then this is probably a bug in the Stack Exchange system. So in that ...
I can't understand why regular users are denied to have a link for tools there, since the link can be accessed anyway at http://www.askubuntu.com/tools.
But, I just made the following userscript that can be helpful in this sense:
// @name Tools link for Ask Ubuntu
// @version 0.1
// @match http://askubuntu.com/*