Story Composure - making sure some nature description doesn't get the reader snoozy or there's too many dialogs that you can't tell who said what.
Style Consistency - seeing as to an angst story tends to be read and interpreted as one, and not lose it's overall style.
Overall style - deleting repeated words, finding synonyms, giving poetical interpretations of otherwise lewd situations ;)
In-universe inside jokes - as in featuring a flute in a Kannazuki No Miko fic ;)
Naming and summaries - A name and summary are what makes a person want to read your story and not someone else's. So thus they have to be catchy or reflecting your true story intentions.
De-anatomizing lemon - making a lemon look like a written romance, rather than an anatomy sketchbook.
Overall lemon - advice, interpretation and ext...
Cold Weaponry miscellany - I'm a little into this, so making use of proper weapon terms and weapon uses inside a story.
In the end if you're totally hopeless, I can come up with plot-concepts for a story...
As a beta-reader:
I'm a soft person on most occasions and I rarely do harsh critique. And in the end I'm willing to work until an author is totally satisfied with his or her story. In the end they can always send me away and do the story their way. I won't care...