^^ I thought about the photosynthesis angle as well.
Zombies flying would be ridiculous, but zombies spontaneously developing a perpetual, self-sustaining energy system is totally believable?
No, just easier to spin. You can say that the Zombies are eating rodents or bugs when no one is looking. Or perhaps they are absorbing or somehow feeding from the very bacteria that would cause decomposition. There's really no good way to spin a flying Zombie (so to speak).
Requires energy to move the muscles in a human body. Zombies aren't eating, or at least aren't getting anything from it, as stated above. Where's this energy source? Perfectly believable under current laws of physics that the virus could provide a boost, and this would keep the zombies going as it burned through all the reserves and the zombie ran out of gas eventually. Not something that can be maintained forever, though, unless the magic virus also has the key to unlimited energy sources that require no input or fuel to maintain.
Maybe the Zombie outbreak was the result of cold fusion experiments gone awry.