This New York Times Article, written by an anthropologist who specializes in epidemics, has a beef with the movie's plotline. The scientific advisor to the movie crafted a scenario in which a bat virus transforms in pigs and is transferred through a handshake from a meat-handler to an unlucky American. Though it's very true that zoonotic diseases (animal in origin) can infect humans this way, the author of the article claims that the film totally ignores natural selection, since a virus in bats is unlikely to be so transmissible and deadly in humans. She cites both SARS and Nipah (the real virus the movie pathogen is based off of), which recombined in domestic animals and in most circumstances are only ineffectively infectious in humans.
This makes a lot of sense to me, but at the same time, I think it's possible (though unlikely) to have that one mutation that's hugely successful and becomes a worldwide epidemic. Existing zoonotic viruses change virulence, since often they doesn't cause illness in their natural hosts (e.g. bats) but causes illness in humans. After all, isn't that how mutations work? I'm a little scared to see the movie, though.
On a side note, the Nipah virus is of the Paramyxoviridae family. It's natural host is in bats but it's often caught from pigs by pig farmers. Symptoms include brain inflammation, flu-like symptoms, and respiratory distress. Disease outbreak is rare and there is no treatment. Link to WHO fact sheet on Nipah virus.