For us, it was the extreme "out of sync" behavior- we started with an IQ test, then a neuropsych and language testing a few years later.
DS was solving shorter math problems years above his age, but was melting down over much easier problems that contained more words/ steps. We discovered ADHD and language impairments.
When an eight year old can remember 48 digits of Pi and all of the elements on the periodic table-- yet have to be told literally ten times to "please get dressed" and "please focus on what we need to do right now" it could be a twice exceptional situation.
Unfortunately, I'm on my iPad so can't paste, but there is an article on SENG about twice exceptional children. It's written by a neuroscientist- I thought it had great information and described the consequences to the child.
We're dealing with a situation now where I feel DS is being held back on harder concepts due to his carelessness. It's having the unfortunate effect of de-motivating him toward his favorite subject (math). We're going to diplomatically introduce the concept of scaffolding during our teacher conference.
