re: a link to the anchor of comment's parent within the current page
it would be helpful if, in addition to the parent link in comment that points to a separate page, there were a link that jumps to the parent comment on the same page. Downside: there may be many equally-useful little things like this which, if all included, would produce a very cluttered interface. My initial intuititive judgement, however, is that a same-file-anchor link would be useful enough to outweigh its associated interface clutter. Associated problem: determine link name that is intuitive and isn't confusable with the purpose of the existing parent link.

re: GUI component: vertical nesting lines that connect two directly sequential comments
these would serve to guide the eye when determining if two comments are replies to same comment. This would be analogous to the lines connecting folders in windows explorer. Additionally, hovering over a line could cause 2 small buttons to appear under the mouse cursor that would jump up to the comment at the top of the line and down to the comment at the bottom of the line. Downside: more visual clutter. However this downside could be mitigated by making the lines be only slightly darker than background color. Downside: GUI is more complicated.

re: help for various UI elements such as the comment-display-settings form above a discussion
I believe a small "?" or "what is this?" link situated near some elements is needed. The link would connect directly to the anchor of the relevant section of the FAQ or other help page. I this this is needed for casual and first-time users. The comment-display-mode names like nested and threaded are examples of UI features that are insufficiently communicative of their associated functions for casual users and beginners. The nearby "?" link would not be intrusive or cluttering if only included for necessary UI elements, and its position/font/size is well-balanced with the UI element.

other topics:
preserve logical structure of displayed comment relationships
    keep links to below-threshold comments in their hierarchical positions
    rather than keeping a single link at the end of a reply sequence
    solves problem where the comment lineage of referenced issues in a reply to a below-threshold
        comment are unclear and annoying to find
display below-threshold parents of above-threshold comments
    there have been several times I wanted to see the parent of high-moderated reply
    but found the link path to desired information to be too annoying/confusing to navigate
needed explanation of behavior of implicit full-comment-threshold for threaded mode
    apparently is unmodifiably set to 4
    apparently unrelated to regular threshold parameter
UI element at bottom of a posted comment that can jump to (great)^x grandparent comment
    why is this not documented in FAQ
    or am I simply misunderstanding something or missing some information somewhere
link to a comment's own cid page
    following the reply-to and parent links at bottom of a posted comment
what is the purpose of the parent link at the bottom of a posted comment?

On your user page that shows all your comments and their ratings, it should indicate how long the comment was available to be moderated, how many posts there were total for that article, and a pie chart break down of how many of each rating (+5, +4, etc.), how many people moderated, and how many mod points total were spent. That way you can get an idea of how many people evaluated your post. Science Daily should have a slash box, it's certainly a better online publication than New Scientist or whatever. Wikipedia should also get a slashbox