1. Money. If your character is using money, you should explain how they get it. You can't just have him appear out of thin air and toss across money like he has a full bank in his pocket. This really bugs me when I'm reading a book in which the character has no way of earning money. There isn't a lot of money in Imaginary Friending.
2. With creatures non-human, there should be some bodily needs explained. Do they need to eat? Personally, I always found it weird that in Twilight--Edward never needed to take those mortal moments that Bella always seemed to. He didn't need to pee? Vampires don't need to pee? They drink blood.... He seemed to have equipment that could serve that purpose.
Okay, so his fangs apparently never wore out or needed dental work--but the dude was drinking blood... what kind of breath would that inspire? He could brush his teeth. Plus, maybe a shower every so often wouldn't be amiss. I'm not saying that there should have been peeing moments in Twilight, but she kept mentioning Bella's as if she was some human freak job because she did.
3. Clothing. Seriously... clothing. If you have a shapeshifter, they're going to be naked most likely whenever they shift back. If you have an imaginary friend that is sometimes visible... why is his clothing disappearing with him? Does he have control over the visibility of his immediate area? Plus, if your whatever gets in a fight while wearing clothing--even if they/it are invincible--is their clothing?
4. Sleeping. Either they need sleep or they don't, but don't gloss over it. If you have a human... you can't have them going a week without sleeping.
5. Family. They didn't spring from the earth--unless they did. Either way, you should explain the presence or lack of family in a person's life and if you don't feel like complicating your roll call with their characters--still... kill them, have them be estranged, or whatever... but there should be some explanation.
6. Why does everyone speak English? Did anyone find that odd about some of the science fiction shows of the past? Every alien seems to speak perfect English?
7. With critters and non-humans, procreation might be of note. (How are more of them created?) Whether it's knocking boots or turning them via a bite... sometimes it's kind of important.
8. Their lives and jobs and school. Even if you want your characters to interact frequently--they should still have lives. Friends (tv series) always did this and it annoyed me. They seemed to have a ton of spare time to sit around during some episodes.
9. Lost time. I've been struggling to insert the passage of time in my books, so I've been paying more attention to how writers create time jumps so that they're not writing an itinerary of a characters events... and also so the novel doesn't occur over a forty-eight hour period. Some authors do it well... and some just really don't. You can't just skip time without reason... as if the days don't matter. This especially annoys me in first person YA books. When you're a teenager, every day matters.
These are some of the things that bug me as a reader. Maybe I'm nitpicky, but there are rules... sometimes you've created your own details due to the world you've set up... and sometimes they already exist. You can't skip across them and hope that no one notices.
The details... the devil is in them. There was a long but rather brilliant post by Kristin Cashore the author of Graceling. It talks about all the nitpicky little things better than I have.
Still, I'm left wondering... shouldn't vampires have to pee?