These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Marty Stu: Genji, though he's possibly a deconstruction of the type of person the author would have known from her life at the palace.
Lampshaded in the narrative as early as chapter 1; the narrator, when describing his various talents, notes that if she fully described all of them, she'd only make him sound absurd.
Squick: Reading the interactions between little Murasaki and Genji, when you know that he's flat out grooming her to be his perfect woman, can often be hard to stomach.
Values Dissonance: Aspects of the story (Genji having multiple affairs, sneaking around, etc.) may seem odd to modern readers, but back then were expected parts of the life of a Heian nobleman. Well, in moderation; Genji pulls a lot of heinous stuff that was considered outrageous even back then. Like seducing and siring a son on his father's wife...or making plans for Murasaki when she's much too young even by medieval standards.