Snopes.com gives a discussion of possible issues with the original experiment. Evaporation or bowel or body movements for instance. I think the biggest complaint about the experiment is that it has not been reproducible and that the original experiment was flawed. MacDougall only took six measurements and he threw two of them out in his original work. The Wikipedia link you give cites a paper where sheep were found to gain weight at least for a time after death. Dogs are found to have no weight change.
MacDougall and his contemporaries were inclined to interpret their results such that animals simply do not have souls, or have different sorts of souls. But if you look at an average of all experiments cited, it could also be said that the average weight loss up on death averages to zero. 3/4 of an ounce of a human being (or a sheep) over the course of something like a death is not an easy measurement. You can't give them a drink of water, you worry that they are breathing too much and losing water. Its not an easy experiment, at least for human beings where you can't control the circumstances of death so well.
In any case this really needs to be measured better. In 90 years it doesn't seem that there's been a real rush to do it.
I just stumbled across this blog post that talks about an effort to measure a change in blood flow to the brain when in intense mental activity popularized in the late 19th century. The investigator Mosso claimed he measured a difference, but the result is disputed today. It could not have been more than a few grams. In any case a description of how difficult this measurement can be.