I've read elsewhere that the director of the show did intentionally base Dr. Brennan's character on "an aspie friend" as he put it. And the actress who plays the character does appear to go out of her way to portray Dr. Brennan as someone on the Autism spectrum, in certain specific ways:
1. She's clearly uncomfortable with eye contact. On the show, she's typically looking everywhere but the other person. The way she moves her eyes is very common with Autistics.
2. The tone and tempo of her speaking is unusual to neurotypical people.
3. Her social awkwardness in detecting and understanding nuance in other people's emotions. Sarcasm usually goes right over her head, but I seem to recall a few lines in there about her struggle to understand it better.
4. She has her core obsessions in her field, but like a lot of TV scientists, she "knows everything about science". This is more of a TV Trope than it is an aspect of her Autism. Most Autistics are the exact opposite, and hyper-focused.
5. Scientists and engineers are more likely to be autistic than the rest of the population, or Autism Causes Vaccines (I wish I could post a link to that SMBC strip, but the board won't let me). 
Other people have said that she can't be autistic because she *does* have friends, but that's a red herring. Lots of Autistic people have friends, especially when they're very smart and they work in a field that highly values intelligence. Like science or computers. Her social awkwardness does strain these relationships, but nerds (and I mean that in the most loving way, as I identify as such) have a tendency towards being quite accepting of other people's eccentricities.
Another way that people think is evidence that she's not autistic is her own capacity for feeling or expressing emotion. Again, this is just a common misconception. Many (most?) people on the spectrum actually have trouble with emotional regulation. They either feel their emotions much bigger than everyone else, or they have trouble expressing it appropriately.