Lew, this is a great thread. On another photo-related site I was frequently in the various image gallery forums providing C&C. It probably should be added that the motivation to post in an image gallery forum is not always to get C&C (some people just want to share and don't want detailed critiques). As such, I always remind people that if they WANT C&C then should (a) specifically add a comment to their post to ask for it and (b) promise not to melt if the C&C seems overly critical.
I try to avoid overwhelming someone with too much advice. It's sort of like learning a golf swing... if I give you 27 things to keep in mind while you do that swing... there's just no way you'll remember all of that. So I try to look at the top 3 things that would have improved the image (even if there many more comments that could be made) -- and typically if the person posts more than one image, I'll look for the commonality of what needs improvement.
In addition to limiting myself to just 3 things that they may need to improve, I try to find at least 1 thing that they did right in order to reinforce the good elements of their work (otherwise they don't necessarily realize they did anything right.)
I do see an abundance of images that are what I think of as "a basic snapshot" -- which appear to have been captured without much thought. I try to encourage new shooters to try read, digest, and post an image that LOOKS like they are actually at least attempting to create a good photograph (it's unfair to ask for a well-written critique which may take some time to write... when it does not look like the shooter even invested as much effort to create the image.) WHEN I ignore an image (yes... we do look, you get "views" and yet no comments... and sometimes that's deliberate) it's often because I felt the photographer did not make enough of an investment in the image to merit a comment. The point here... for those who actually do WANT good feedback... you need to WORK on your image as though you are actually making a real effort to improve.
For those photographer's who have read the foundational instructions on basic exposure concepts (e.g. Bryan Peterson's "Understanding Exposure" for example), then I'd recommend moving on to understanding composition next... e.g. Michael Freeman's book "The Photographer's Eye -- Composition and Design for Better Digital Photos" is a good book for this.)
You mentioned critique about whether the image is able to convey a feeling or mood. And for this, I think lighting (which gets far too little attention in photography... which is ALL ABOUT LIGHT) is high on the list of things a photographer needs to learn. I see all too many "I just want to use natural light" (frankly some of the best "natural" light imagery you may have seen... probably involved supplemental lighting and lighting modifiers by the photographer and was not a happy coincidence of finding the right light... it was about making the right light.) Then they want a new lens and nobody ever asks about lighting (well... a few do). Lighting will do far more to improve imagery than a new lens.
Use of lighting, contrast, high-key vs low-key, etc. can all be excellent tools to convey a feeling of solitude, or joy, or despair, or calm, or... whatever. Name the emotion and we can probably name a way to configure lighting that would help convey that. You've mentioned the use of color and saturation (or de-saturation as the case may be). I like to use moderately subdued color or softened images to convey a sense of beauty. But if I want to convey excitement or high-energy I might go for more saturation and harsher contrast to give an edgy-feel. These are not "rules" so much... I think the more important concept is to consider the situation, what you want to convey and evaluate what sort of adjustment would fit the situation better. I do see photographers who want to develop a "style" and apply it everywhere. I prefer to apply adjustments based on what I want to convey and not blanket the same "style" onto every image as if it were my own personal brand.
I learned photography by being an apprentice to a professional photographer when I was 15. One of the best pieces of advice he ever gave me (and really helped me learn) is that whenever you're exposed to imagery... reading magazines, or wherever you find them. As you skim through the images, you will occasionally find an image that has "stopping value". This is the term we use to describe when an image has something about it that makes you pause and look at it for a longer amount of time than you looked at any of the other images. When you find that "stopping value" image... study it. Understand WHY it made you pause... why did you pause on this one, but not pause on the image just before it? Break down everything you can ... it's composition and balance, modeling and posing, lighting, mood, and energy energy, rhythm, patterns, and flow, you name it... study it. Imagine you would have to re-create that image ... what lighting and light modifiers might you need? Where would they need to be? How would you ask your models to pose? Etc.
BTW, on the other photo-site (the one where I was posting daily constructive comments in the galleries)... what I think became a drain was taking the time to describe how to improve the image... only to have the photographer go out and just shoot more of the same. It made me wonder why I ever bothered to offer constructive criticism beyond "that's nice".