Just finished, but there isn't too much to tell you because only half of chapter 2 is out (so still common route). Obviously the theme is that you can't remember who you kissed that night because you were so drunk you have no idea, and now you're trying to figure it out, so if the kiss alone counts as cheating you won't like it but your character can feel really bad about it (although the game won't let you tell him just yet). You can fight with your boyfriend (unrelated to the kiss) so I'm hoping that you would be properly broken up before starting routes with any of the other boys but the game isn't out that far yet.
There are some mildly flirty options with some of the boys but they're pretty avoidable and most of the time it's really just play flirting, a lot of the characters do it with each other too.
All in all I did really enjoy the game and can't wait for more but I think not enough is out to decide how exactly it's going to deal with cheating/breakups.