Is it common for a child with autism to have some sort of eating disorder?

Picky eaters. The most common abnormal eating pattern seen in children with autistic spectrum disorders is having a very narrow range of types of food he will eat. It's the picky eater of childhood taken to the extreme. He may refuse a certain food based on its texture or consistency, regardless of flavor and smell. Dealing with chronic constipation is a common challenge. Try to get a daily multivitamin in him.
It can be an issue. I have to put this out there: if you have any concern that your child may have an asd, don't introduce him/her to chicken nuggets! if we could figure out how to make healthy food taste like chicken nuggets, there would be a lot less obesity in children, high or low functioning, who have asd's. They generally " like the whites, hate the greens" & reject foods based on color, texture, odor, or all 3.
Also PICA. In addition to the other comments here, pica, which is characterized by an appetite for substances that are non-nutritive, such as clay, chalk, paint chips, plastic, dirt, or sand, is not uncommon with spectrum disorders. Pica can also lead to complications including lead poisoning, abdominal obstruction, iron deficiency and other findings.
Not the disorder. Children with autism can be quite sensitive to certain things and stimuli including food sentitivities (likes/dislikes/overindulgence). They can be quite picky in what they eat, wear, etc. Eating related difficulties resulting as part of the autistic behavior are not considered as eating disorders.