A lot of good comments up above, but I would add that maybe you could look at submitting personal ads for him…and agree to supervised meet ups with other mentally disabled people that are in the in-between zone your brother seems to be in.
I hope it's not too much of a spoiler if I say that I agree with the mother's eventual decision, which mirrors the comments in this thread, only with a much lusher score. Otherwise she likes caring for Alzheimer patients, going to church, and staying home with her parents. To be more serious though, my uncle was severely mentally retarded and he had his share of "girlfriends". What I might consider, taking shots in the dark, is that she simply may feel comfortable with this man: I immediately took mental disability as retardation.