Be careful about falling for a false "cause" that is just another symptom of the underlying cause of both problems.
For example, you'll read in Boyd Haley, former chair of the chem dept at the U of KY, and Andrew Cutler, PhD chemistry, author on detox, that mercury is a likely cause or major contributing factor in most cases of Alzheimer's.
Haley says the three hallmark indicators of Alzheimer's--neurotangles, beta amyloid plaque and tau protein problems-- can be created in the lab from mercury's effects on the brain. For example, this video from the U of Calgary shows the neurotangles of Alzheimer's after introducing mercury into snail brain tissue. http://www.youtube.com/watch?v=GDnfeIwd0wI
However MS is very vulnerable to heavy metals including mercury. My understanding is that MS's contains zinc. Zinc and mercury are somewhat similar. They are congeners in the periodic chart. They compete to some extent; however, mercury is the big bully. It displaces zinc in various body chemicals thus damaging the chemical's functionality.
So even if a person has adequate amounts of B12 and methylfolate, the mercury-inhibited MS enzyme will keep homocysteine from being converted to methionine at a normal rate.
Dr Amy Yasko, PhD chemistry, touches on this issue at the following site on Autism.
"Another one of the enzymes critical to methylation, methionine synthase (MTR/MS), requires an active form of vitamin B12 in order to function properly. The body's ability to supply B12 can also be impeded by the MTHFR mutation. Further, research has shown that mercury adversely affects this reaction...With both the mrcury present...and the MTHFR mutation you now have two accidents ... causing a roadblock (impaired MTR/MS function.)" http://www.dramyyasko.com/resources/autism-pathways-to-recovery/chapter-2/
Note there are strong links between mercury and autism, for example:
Autism Research Institute treatment parent ratings 2009 http://www.autism.com/index.php/treatment_ratings_asd
"Detox. (chelation)" 74% report "got better", 3% report "got worse", 23% report "no effect"
The 74% rating is the best of all of the many dozens of listed interventions.
There is SO much more that could be said about this issue. When you see the list of Alzheimer's symptoms, so many of the symptoms are also present in sickly younger people who get much improved by heavy metal detox. I've seen this in my own detox experience and in so many cases in the detox groups, especially Cutler Protocol support groups.