I totally agree that sex shouldn't be included (especially when it's explicit--implicit is a lot more acceptable. It's just... I've read some YA books that were basically erotica and that makes me so uncomfortable). I don't mind romance, though! I used to hate it, but now I like it a lot, as long as it's secondary to the plot (and as long as it doesn't contain too many boring hetero tropes... like a guy swooping in to rescue a girl, etc. Or obvious, try-hard subversions of hetero tropes, like a girl swooping in to save a guy). Names get me, too. If they're too silly, I put the book down. (If they're based on something that's relevant to the story, though, I don't have an issue. Like, my characters' names occasionally look a little odd, but it's because they're drawn from a foreign [and also dead] language.)
The WORST thing is when the author totally misunderstands medieval European society, but still attempted to write it. Maybe it's because I adore medieval history, so the errors are more obvious to me... but I hate it so, so much. It physically pains me when someone clearly did not even attempt to research. (Honestly, an obvious lack of research in general is awful.)