For magic and stuff, I think Brandon Sanderson has it right. The more you define the rules of your magic system, the more credibility you have when magic does something that affects your plot. And in general, with fantasy, credibility as a good writer in general means a lot to me. Which means I'm going to accept some weird stuff if you write it well and hook me, and won't accept even basic stuff if the first chapter or two are boring and badly written and inconsistent.
What matters to me more than the physical is the social, though. I enjoy social dynamics a lot, so if the interesting social ramifications of something are totally handwaived or ridiculously contrived, I'm likely to lose interest unless the writing is really good. For example, I've read like three urban fantasies now where people know vampires/werewolves are real, the police have their eye on them, and it's allegedly modern America and the supernatural don't rule openly. In all three, the vampire alpha males (always a cheesy alpha male) did whatever the hell they wanted, could force people into their societies against their will, and didn't bother to hide the fact that they were running things like mob bosses or vigilantes. And the cops never intervened despite it being more brazen than even Capone attempted, and the heroines never just said, "No, f*ck you, I have Constitutional rights and proof that you're threatening me and you're going to jail." I could buy that if the vampires had like, infiltrated the government with mind controllers or something, or it was a corrupt dystopia. Modern America, where the alpha male vampires are famous celebrities? Much harder to overlook, especially when explaining _how_ the vampires get away with this shit in plain sight would be more interesting. I'd much rather see a little more drama about how a society like that co-exists with the real world rather than a lot of handwaving and "eh, everybody just accepts it cause genre, here's a katana."
(Oh, and speaking of those books? If the heroine who has never been in a fistfight in her life is able to beat up supernaturals who have fought each other for centuries, she needs some cool special trait to explain it. "I took self-defense classes for a few weeks so now I can beat up werewolves who have the same powers as me and decades of combat experience" doesn't cut it, but "I have some weird trait that makes me many times stronger than them or gives me inherent fighting skill" is fine.
EDIT: Also, as a lesbian who is also transgender, I'm kinda interest in LGBT people being portrayed realistically. Instead of exploitative gay best friend stereotypes and stuff. I'm looking at you, two out of the three books I mentioned above.