I think her treatment of Zac really ruined her characterisation. Up until then, I thought she may have had potential. The main problem is that she acts very immature, and unlike Maddy, does not have the benefit of youth to explain her behaviour. But she was horrible to Zac after they broke up, which was not in keeping with the fact that she supposedly really cared about him, and they broke up because of the twins rather than any inherent problem with their relationship. It was even worse for her characterisation to pair her up with Andy and make her choose Andy over Zac - it made no sense given Andy's characterisation up to that point, and her history with Zac. It just made her again, look immature and shallow like she could only handle a physical relationship. Even now, it seems Hannah is more interest in the physical stuff with Andy rather than any emotional connection.
It seems that Hannah spends a lot of time claiming that she shouldn't get with a certain person (Zac, Andy, Nate) only for her to show no self-restraint and get with them anyway. Again, making her appear very shallow and fickle.
The problem is that we are meant to see Hannah as a likeable character, the type of girl that would make Andy want to change his ways. But instead, we have this immature, shallow character who lacks any of the warmth of other characters such as Leah.