If a comment is flagged, do moderators normally look at only the comment, or also the general context of the comment such as what the comment was replying to?
Given that I am the current grand-champion for deleting comments, perhaps I should address this. Note that other mods may hit your flag though and have other strategies. Hopefully it all evens out in the wash.
Yes, when I field a flag for a comment, I look at all the other comments on the same post.
For one thing, sometimes a person simply doesn't like what a comment has to say and wants to trick me into deleting it. I'm looking for that.
Other times, the comment may have become obsolete, so I'll check to see if the post has since been edited in a way that essentially surrendered to the comment. In that case, the comment should go.
Other times, the comment is chatty. Usually this will trigger a move to chat, and deletion of it, all other chatty comments, and all comments in the same conversation.
Sometimes the comment is "not nice". In that case it gets deleted, responses to it get deleted, and any less-than-fully-nice comments leading up to it get deleted.
And sometimes it is just such a huge mess that I'll "declare comment bankruptcy" and delete them all. If I can move them to chat first, I might.
That being said, if some injustice is done to a comment, well that's the way the cookie crumbles. Comments aren't our product here, questions and answers are. Don't expect comments to last forever.
I once had a friend who made a distinction between "house cats" and "barn cats". House cats are pets you care for. Barn cats can be cute and helpful with pest control, but they have all sorts of misfortunes befall them; stepped on by livestock, eaten by wildlife, run over, threshed, baled up, etc. That's just life. You don't get attached to them.
Comments are our barn cats.
I may not be the ideal person to answer, because I have only been moderating for a week or two. I need to understand the context of the comment before acting. On the other hand, in my limited experience, context has not been a discriminator. That is to say if a comment needs to go, it needs to go. While I have consulted context, it hasn't been relevant.
The comments I've deleted have either crossed the line into acrimonious debate, (in which case I'm going to delete the comment without reference to context), or have digressed beyond the attempt to clarify the question - in which case I'm going to delete without reference to context.
That answer feels a bit like Tevyev from Fiddler on the Roof - "they're both right.", but like Tevyev, it is at least sincere.