My nephew has Aspergers; he has not been to WDW, but I can give you some information about Haunted Mansion based on things I know he would not like or would have probelms with. You might also want to visit the disABILITIES Board for more information. Some of the regular posters to that board have Aspergers or have children with autism or Aspergers. There is a link to the disABILITIES Board in my signature.
If it would help you to see what the Haunted Mansion is like, there are videos on
youtube that show pretty well.
This one is very good for color, but not so good for details.
Here's
another one that shows a bit of the queue, the preshow and the ride. It is much darker in the ride, especially in the preshow than it looks in the video.
WARNING: SPOILERS AHEAD> DON'T READ ANY FARTHER IF YOU WANT TO BE SURPRISED:
The Preshow:
The room will be quite filled with people and the CM tells everyone to go to the 'dead center' of the room. If you have problems with closeness with strangers, have members of your group act as a buffer between you and the other guests. At the end of the show, the lights go off and you will not be sure which way the door to get out is. In the video, it shows a crash of lightening just after the ghost host says "There's always my way." You might want to hold hands with the rest of your group then so you don't get separated in the dark. There are some loud screams that are part of the preshow and some guests usually scream too.
The Boarding area:
It is pretty dark when you get into the boarding area. It starts out fairly wide and the path gradually gets narrower and narrower until the guests are divided into a single file row. There can be some pushing and shoving. I would suggest that you and the rest of the people with you try to wait in the preshow room until most of the other guests have left if you can. That way, there won't be as many people pushing against you to board.
The Ride:
It is very dark in spots. As people have written, it is mostly funny scary.
There is one part where your ride car will be turning around and going backward down a hill; that is just before the graveyard. In the graveyard scene (starting at 5 minute 55 seconds in the video I linked above), there are a lot of ghosts popping up and screaming. The video doesn't show it really well because you can't hear the screams real well and the ghosts popping up look slow. In real life, the screams are much louder and the ghosts pop up more suddenly. Some people don't like that part because it is so un-expected.
Near the very end, you will see your ride car in a mirror and there will be a projection of a ghost in your car with you.
My son has Aspergers too. Last time we went to Disney World he was almost 12 and didn't think Haunted Mansion was scarry at all. He says the scariest part to him is the streaching room in the beginning before you even get in your ride car. Mostly I think people scream in this part to scare each other. He loved Tower of terror and Expedition everest. 
LOL But I am a bit of a wuss. Haunted Mansion is more 'campy' scary than truly scary. I am *hoping* my 2.5 year old doesn't get the pants scared off of him b/c we're planning to have him ride it with us....I guess we'll find out.....
Have fun on your trip!
