my DS has anaphylactic allergies to treenuts, peanuts, milk products and eggs. He now can tolerate small amounts of whey and sodium caseinate at age 15, but when he was little I ended up in most of the disney kitchens, including the grand floridian to check ingredients.
We have taken him to DW 5 times, and our experience has been mostly positive. We were there during the very busy second half of August this year, and had more frustrations than usual.
3 of the "direct to the restaurant" numbers the central reservations office gave us turned out to be incorrect--I don't know if they've been changing extensions, or if she needed her reading glasses adjusted. I discovere when we checked in that she'd put "lactose intolerent" rather than "immediate death milk allergy" on the PS's, and had noted the peanuts but not the tree nuts.
Normally the chefs are very accomodating in terms of asking what they could fix--this time they all walked us through the buffet--but on 3 separate ps's they had not fixed the alternate potatoes or rice we'd requested, so our DS would have been waiting a long time after we'd been served.
All in all my DS felt on this last trip that folks were accomodating in terms of making sure he didn't get food that would harm him, but didn't seem to be leaping to provide tasty and creative alternatives.
At Boma, the chef did clean the grill and make him a special dairy-free salmon--but the last time we'd been there, the chef had made him a sorbet and fried papaya pastry, so we were disappointed when they produced the Rice Dream (unfortunately my DS thinks it's vile.)
My bottom-line experience is that the sitdown restaurants are your best bet. Even then--if it's anaphylactic reactions to hidden traces of any common product, you need to do the same careful reading of labels that you do in the grocery store. I was shocked to discover the turkey breast contained nonfat milk at one location.
If you are going to eat at a buffet try to eat at a less busy time--when they can be more attentive--and if it's the Crystal Palace, i would highly recommend sauntering by about an hour before you PS to remind them to put that plain potato in the oven, or whatever you've requested. It's not so hard for our DS now, but when he was 6 or 7 it was very painful to eat at a place with 20 mouthwatering desserts laid out and to discover he couldn't eat a single one.
Our best buffet experiences have been at the GF ParkFare, and Donald's Breakfast-osaurus in AK. At Donald's they made him dairy free pancakes--the first he'd ever had. Boma is normally very good, except for this last time when they were over-busy. On a previous experience at Crystal Palace they made him a dairy free brownie.
We have had terrible experiences at Chefs de France--which served a product with cheese in dim lighting (which would have killed him if he'd taken a bite), and at Morrocco, which helpfully produced a list of "safe" foods for someone who would be allergic to everything, and had 4 items on the list--and did not even try to differentiate between what he could eat with his specific allergies. The Coral Reef this time had a server who didn't speak english well and screwed up the order. Be aware that at both Coral Reef and Canada that if you order the sorbet it comes garnished with products containing nuts and chocolate. This time even the Brown Derby seemed a little put-upon in subbing fries for the milk-laden potatoes. The server then left off a sauce which he could have eaten because "he didn't want to take chances" and sort of flipped his hair around when we sent it back to be sauced.
We did not even try it this time, but Ohana's was one of the worst experiences we've ever had, on our last visit. It was completely due to our server, who didn't want to interrupt her spiel long enough to even get the chef, and who insisted there was no milk in the caramel dipping sauce--we knew better, but it got his hopes up. She then CHARGED for whatever dessert alternative (a frozen icee drink) she finally came up with.
Our best sit-down experiences this time were at Cinderella's castle (lunch) and Mama Melrose's, which went out of their way to be tasty and accomodating.
If I may be of any help, feel free to PM or email me. I believe we've eaten in most of the WDW restaurants over the years and all of it has been with the food allergy filter assessing the experience.
But I have had some excellent meals). 
