This movie clearly has some dramatic license, the question being how much. As to the destruction of the library at Alexandria. The immediate question would be if some pagan library or center of learning -- not necessarily the original one -- was around to be destroyed. One modern account:
Alexandria underwent a slow decline beginning in 48 B.C., when Julius Caesar conquered the city for Rome and accidentally burned down the library. (It was then rebuilt.) By 364, when the Roman Empire split and Alexandria became part of the eastern half, the city was beset by fighting among Christians, Jews and pagans. Further civil wars destroyed much of the library’s contents. The last remnants likely disappeared, along with the museum, in 391, when the archbishop Theophilus acted on orders from the Roman emperor to destroy all pagan temples. Theophilus tore down the temple of Serapis, which may have housed the last scrolls, and built a church on the site.
The last known member of the museum was the mathematician and astronomer Theon—Hypatia’s father.
More research would have to be supplied for me to learn if such "pagan temples" were also centers of learning, though I would not be surprised if they were. Looking at the entry for Hypatia at Wikipedia, there is an extended discussion, well documented, about her life.
So far, I have not found much on the destruction of the library, but more on her death. This includes more than one account where it is cleared she was murdered (one Church historian used that very word) by some sort of Christian mob, directly or indirectly a result of a power struggle between a local church official and secular authority.
As noted by the article [I reference the review over at Slate], the movie is somewhat suspect on dramatic storytelling, and we do not get much of a sense of Hypathia's full career and teachings. For instance, she is a follower of Neoplatonic philosophy, which influenced some Church thinkers -- including one portrayed in the film. After the destruction of the library/temple, it is not quite clear how H. spends her time. Looking over some historical accounts, it seems she did continue teaching and/or her studies, though the movie is pretty vague on the point.
Also, more probably could have been shown to explain why Christianity was winning out over the pagan elites. One scene showed the feeding of the poor, but that is not really enough. Was Hypathia in a type of "ivory tower," her philosophy of doubt over certainty not a good fit for the troubled times? This would be an interesting conflict to examine.
The movie is worth watching. It is about something, more than one thing actually, and the lead performance is quite good, though it could have be written a bit better. The supporting roles are somewhat of a mixed bag, at times overly simplistic. We get a sense, imperfect or not, of a different place and time, and overall benefit from the overall experience.