Designated Hero: Although it is possible that this was invoked for Author Tract, not many fans perceived Hiromi as a good character, more considering her a jealous jerk that offended Noe even when she believed that they could not be together with Shinichiro.
Idiot Ball: A dramatic Love Triangle would never have happened if Hiromi immediately told Shinichirou that she was ignoring his feelings, because his mother said that they were brother and sister and subsequently Shinichirou could find out from his father that it was a lie.
Again, this is the first work in the original script of Mari Okada, whose ending provoked anger among the fans.
Narm: The constant talk about tears can come across as something very creepy.
The Scrappy: One of the main complaints with the series is that Shinichirou, the protagonist, is too bland. And that his obsession with Hiromi's tears is cranked up to serial killer levels. Another prospect for future serial killer levels of creepiness is Jun, Noe's brother, who acts like an egoistic jerk throughout the entire series.
Additionally, Hiromi is often hated for being slightly less interesting than the other girls on the show. Thus when she got together with Shinichirou, the resulting backlash bore out from the Shipping Wars.
In relation to the above hate against Hiromi, fans also despise her for her very subtleJerkassattitude towards Noe. Her selfishly telling Noe to go away and to leave her and Shinichiro alone because they reached an understanding while Noe was still in a relationship with Shinichiro was the boiling point of the fans', especially Noe's (and there are a lot of them), hatred towards Hiromi.
Stoic Woobie and/or Jerkass Woobie: Depending onhowyouviewHiromi, she's either one of these, or both of these since her life hasn't been easy for her at all regardless of her attitude and actions in the anime.