A pretty extensive article can be found at
http://www.snopes.com/religion/soulweight.asp. Snopes and similar sites are usually pretty good sources for digested research on this sort of question.
Creating a scale to give a very precise weight of a living (or, I would presume, dieing) human being in open air is challenging. Normal lung dynamics result in about +-5 g of mass loss, not including the jet effects around the nose and mouth. Blood flow is irregular, and involves a large mass moving surprisingly fast. Small, involuntary musculoskeletal movement can cause forces in the kilo-newton range.
To have any hope of measuring the famous “21 grams”, I believe you’d need to have the dieing patient in a sealed chamber with all their breathing gasses and fluids, and take many closely-timed weighs of the whole chamber with a few grams precision.
However its done, It’s a daunting and expensive-sounding bit of engineering that I don’t believe MacDougall accomplished in his 1907 experiment.
If you had the apparatus, I doubt you’d have any ethical problems using it – plenty of terminally ill people don’t need much medical care, and would volunteer “to die for” science. You could probably get the
Randi Foundation to send observers, though I wouldn’t count on winning the $1,000,000.
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