I keep seeing questioners answering their own questions with an update instead of editing the question. Is this maybe a problem of a not prominent enough edit link? Since this site heavily depends on editing, we should make sure that people find it.
I don't think the problem is due to how well the links stand out but how well people are acquainted with the format of a Q&A site such as this. Some newcomers seems think of this as no different from a conventional forum (while it's not, see https://askubuntu.com/about) and therefore act as such. Thus, actions such as answering one's own question to provide details instead of editing the question or posting a comment as an answer may rather be the mistake of treating this site as a forum.
So, the solution to this problem is not, I think, to change the appearance of the links but to inform newcomers of how to use this site. This can be done via comments, flagging and also by discussion in chat. Maybe we should give pro-forma coomments that describes how certain aspects of this site works a push?
Finally, I think the appearance of the links are good as it is. It's good that they don't stand out too much so that pages look less cluttered. If you understand that each post can be edited you'll know that there are links below each post.
Adding Hint Text Next To the Answer Box
I just had an alternate idea I'd like to add. Perhaps the problem is not with the links, but the answer box itself.
Here's how the top of the answer box currently looks:
To a newbie, there is nothing overtly obvious about this that suggests this is where you post the answer to your question. "Your Answer" could just as easily mean "Your Answer To The Previous Post", like in a forum. This could be a potential source of confusion.
A possible solution for this is to use some hint text that reminds the user what the answer box is for. Below are a couple ideas I just quickly made up in GIMP for what this could look like:
The wording/appearance doesn't have to look exactly like this, but it conveys my general idea.
In addition, if it is possible then perhaps the wording could change depending on whether you are answering your own question or somebody else's question:
Version 1 (someone else's question variant)
The added advantage of this is that it could also help guide users away from misplacing comments on other questions, adding "me too's", etc. I think a lot of these all stem from users expecting our site to work like a conventional forum, and we should help point out to them the differences.
I also think that maybe the tooltips shown when hovering some of these links should be updated. For example, the tooltip shown when hovering the "edit" link currently reads:
revise and improve this post
Perhaps it should be expanded a little to say:
improve this post with more details, corrections or an update