As an author if you are soliciting constructive criticism, be sure to make that clear in your thread that you welcome comments of any kind. However, the same rules apply: we are all guests here on Phillip's board and we should all observe civility, particularly when disagreeing.
I'm still struggling with Chapter 4 of my only fanfic, and would certainly like some constructive criticism as I go along. And there are fairly objective standards for that:
Is the plot clear; i.e., can you readily follow what's happening? Or do you have to keep checking back to an earlier chapter to follow it?
Are the characters' motivations believable? One extra challenge in fanfiction is that the writer is using characters that were already established previously. In a sequel especially, they can certainly undergo changes but that has to be believable in the context of the basic story and basic character development that's already there.
Is the writing coherent? Are there too-mixed metaphors, imagery that seems to come out of nowhere? Does the story meander off too much into subplots whose interest and relevance aren't enough to sustain them? Is there an overabundance of misspellings, misuse of words (e.g., "fulsome" used to mean voluptuous or sexy), really bad grammar when it isn't in the context of colloquial speech? Does the author make points via plot or character development, or do they just preach? If the criticism is more than a few comments, personal messages might be the best option, as that allows for a lengthy one-on-one discussion.
IMO, we pretty much all know what isn't constructive. Comments like "your writing is as stupid as you are" (not written to me) and condemnations of some particular genre, including less-than-flattering character assessments of writers in that genre, obviously aren't going to produce much in the way of improved creative work.
While I've read some fanfiction before, BBM is the first time I've ever looked at it extensively for any one work, and there's plenty to discuss. Thanks for volunteering, Leslie and Louise!