Moderators have access to a widget on posts -- if the browser window is wide enough (I think 1250px is the minimum?), and if your vision is good (it's small and light gray). The widget provides instant access to the number of (and actual) deleted comments and the number of flags. That information is also available via the "mod" menu on posts, but that's pull, not push -- the widget alerts me that there's something to see, while I'll only look at the menu if something prompts me (a new flag, more problem comments, a mention by another moderator, etc). So the widget provides valuable information -- if you can use it. Not all of us can (especially when we're using tablets).
The widget also makes it easy to undelete comments -- purge an entire thread, click the control to see the deleted comments inline, and undelete the handful that should stay. The mod menu doesn't give us undelete. (It's also a separate page, so slower and harder to use.)
Some CM, I think Shog9, said the widget was designed for large sites like the trilogy and moderators of smaller sites aren't the main audience. But as a moderator on some of those other sites, I've found having these controls right there to be very helpful in doing my job. It's so helpful that I asked for help from my fellow moderators in solving my "can't see that thing" problem, and ArtOfCode wrote a userscript. This script moves the information from the widget into the main part of the page, right under the voting buttons. It looks like this:
From top to bottom, that's: number of flags, number of deleted comments, and timeline. Everything fits conveniently within the space the site is already using -- no marginal protrusions needed. If the post is super-short, it doesn't overlap with comments either because those don't extend past the post's left margin. (I changed flag background from the usual orange back to yellow because I can't read the ones that use orange. You'd get your flag color there, whatever it is.)
This userscript works great on my desktop computers, but I haven't been able to make userscripts work at all on my Android tablet. And my tablet is 1024px wide, so I don't get the default widget. When I travel I only have a tablet, which means I'm hindered in doing my job. In discussion with other moderators I've learned that I am far from the only one who doesn't use full-screen browsers; people who use a browser and text editor side by side on a 1900px monitor (still a common size) also don't get the widget.
Feature request: please add the functionality of this user script to SE, so that it will work on all devices without need for userscripting. The back-end work is already done; this is purely a UI matter. It's a moderator tool, not part of the main site design, so it doesn't have to be beautiful; it just has to let us do our jobs.
Please may we have a built-in, accessible UI for this super-useful tool?