[Disclaimer: Possible Spoilers for Fantastic Four movie]
I would like to first state that I have not read the comics regarding the Fantastic Four, so this article will be based solely on characteristics that I noticed during the film.
The decisions made with the character may have been on the part of the writing, directing, or acting choice. However, there are small signs of Asperger Syndrome in the character of Reed Richards.
Problems with relationships
When we first meet Reed, he is in his classroom getting ready to give a report. The kids around him openly mock him, and the teacher does little aside from stating settle down. He meets Ben Grimm and teaches him about the teleportation device he's going to make. As he grows up, he still has a friend in Ben, but he doesn't seem to have relationships outside of him, even telling Sue that he doesn't get along with his parents because they don't understand him.
The way that Reed talks in the movie is definitely a little stilted. This may just be bad acting, but looking at it from this perspective it actually makes a lot of sense. When he tries to make a joke, like how he wishes he was adopted, he says it in such a serious way that it seems almost off putting to other characters. When he sees the reaction he does back track ever so slightly. When Johnny makes a friendly gesture, one that surely he has done before, he doesn't connect it and does something completely different. He is trying, but it doesn't quite work because he doesn't have experience with social interaction. Doom and Johnny want to drink to their success and his first reaction is that drinking kills brain cells. He is factual first, social second.
Specialized field of interest and hobbies
Reed spends the better part of his life working with technology and trying to figure out how to build a teleportation device. All of his energy and focus go into this hobby, and eventually it becomes his livelihood. A lot of the time, someone with the disorder will be very good with their hands and mechanical hobbies, so this didn't come as a surprise. On the same hand, though:
Difficulty making predictions
When he meets Sue and Dr. Storm, they inform him of the dangers of his device. While he had seen that objects could come back through the device, he didn't realize that he was tearing a hole in space. They then tell him that he could have created a black hole that destroyed the entire planet. He looks nonplussed as he says simply that he had no idea and he was sorry. He hadn't thought of what he could do, just focused on what he wanted to accomplish.
Problems understanding another person's point of view/feelings
While he does care about his friend Ben (he must for them to have stayed friends for so long) when they are finally reunited after the accident, Reed isn't even able to respond to him properly. All he seems to be worried about is the fact that he messed up and needed to fix the situation. He is very stilted and tells him he is sorry, but doesn't look like he is really reacting that well and is coming off very cold. It isn't until Ben actually yells at him and says "Look at me and say sorry!", Only than that he truly looks at him for the first time since the accident. He might have still been in shock but it could also have been that he didn't know what to say or how to react.
Above average intelligence
I don't think that this needs much of an explanation. At 10 he was able to at least have the beginning stages of the teleportation device, and had nearly perfected it at 18 when he is able to send inanimate objects to the other dimension and back, something grown-ups were unable to do themselves. He had an incredible mind that surpassed that of men twice his age.
I am not a doctor, and this is the most basic way of describing symptoms of Asperger's Syndrome, but it is interesting to think about.