Nonconformity and questioning of authority
We want our children to learn to think for themselves, and believe that a healthy questioning of authority is a valuable and desirable character trait. But just as most of us would not hand the car keys to a ten year old and tell her to have fun, we should be very careful how much and what we allow our children to decide for themselves without our input and guidance.
All children will test limits and boundaries, questioning the information they receive, asserting independence. But for the gifted child, this quality can often go beyond that of standing firm on her own convictions, or a habit of simple disobedience, because her thought processes function so much differently from others. She will look at a problem from several different angles all at once, and because she thinks in a fairly mature and complex way, she will feel that her decisions are well thought out and, necessarily, right. The gifted child will not stop challenging after a few times, but will remain obsessed with fairness, with logic, with their own feelings at that moment in time, which are neither developed nor mature enough to be trusted.
Simplistically, this could manifest itself in a minor school assignment. I might have my daughter recopy her messy writing assignment (exceptionally sloppy handwriting is another characteristic!) before giving it to me to put in her notebook. She might decide that she would rather just type, but because her brother is using the computer at that time she will put the assignment aside. Having neither asked for permission nor discussed the situation, she will feel justified in her actions because they are, to her mind, infallibly logical.
While in some situations, such staunch independence can be a good thing — for instance, I doubt our headstrong, individual, self-confident daughter will ever "follow the crowd" — there are some obvious and immediate difficulties with this characteristic. It poses a particular problem when we try to teach our nonconforming child to be obedient to their main authority — parents — in preparation for a lifetime of obedience to God.
Another aspect to this characteristic is the very real issue of anxiety in gifted children, often caused by their advanced knowledge. It is important to be very careful about what knowledge they are allowed to have access to, regardless of their intellectual ability as children, gifted or not, are simply not emotionally ready for various topics or details.
But no matter how careful you are your child may be unable to go to sleep or go outside to play because she is anxious about something she has read or heard about. Be careful to treat her concerns seriously, whether or not they are grounded in reality, and remember that she is a child, first of all. While she may have thinking skills far surpassing others her age, she is still her age.

Perfectionism
No one would argue that precision is important. After all, we need only take a cursory glance around us in order to see the precision of our Creator. Anyone who has studied any topic in depth, from life science to Hamlet to nuclear physics, can see that without precision there would be meaningless chaos. Which car would you rather drive—the one put together by someone who had a garage full of junk and some spare time, or the one built by trained engineers who have done extensive research and testing in order to develop the best design and materials?
Many people, maybe even you, may have perfectionist tendencies. Maybe you are annoyed by towels stacked left to right or by the toilet paper that comes from the top of the roll and not the bottom. Maybe someone you love will not sit down to relax until the dishes are done and the kitchen is clean.
As with all of these characteristics, perfectionism is different in a gifted child due to degree. My son was obsessed for a while with precision in our speech. If he asked when we were going to the park, and I could not immediately give an answer resembling "in nine minutes and 42 seconds," I needed to say "in about ten minutes."
This is tied in to obedience as well, because my son, as a default mode, will obey the letter of the law and not the spirit, which is a fancy way of describing a strange kind of extreme legalism. We must say, "You are not allowed to jump, bounce, jiggle, spring, somersault — or any other action that is not sit — on the couch with any part of your body," when we simply want him to quit jumping on the furniture. He is not being a "smart aleck," as another child might be, but is merely being who and what his giftedness makes him. Far from excusing him from his behavior, we must be forever diligent in training him to overcome this handicap.
Unless they are systematically taught coping skills to bring their behavior under control, gifted children may be unable to function normally due to extreme perfectionism. This can take the form of obsessive attention to detail in their schoolwork or art project, or it can be an insistence on a particular work environment, or even abject misery when they lose a game of Uno.
Often, gifted children are accustomed to success, and when it does not come immediately and with ease, they will feel utterly destroyed. Not only is perfection impossible, the gifted child will suffer from failures far more than other children. Because of this, as terrible as it may sound, we have to make certain they fail sometimes, while they are safe in the love and security of home, so that we can teach essential coping skills. Otherwise, when failure comes, which it will, they will crash and burn.