We have seen a number of comments on this, such as what was the water in the microwave boiled in. The thinking is that maybe some leaching took place if it was in plastic. It was boiled in a plastic cup, so this could be a possibility. Also it was not a double blind experiment, so she knew which was which when watering them. On top of that she was wanting the microwaved ones to do poorly, and although most scientists would dismiss the idea, it is possible that her thoughts toward each plant had an effect as well. Bottom line is, the results are interesting, and duplicate the results that others have reported (try Googling '"microwaved water" plants') more experiments need to be done with better controls and as a double blind study. But this was a simple 6th grade science fair project, and was never intended to be anything more than that. The plants were genetically identical, they were produced from graphs from the same parent plant, so that variable can be eliminated.
Intriguingly, the Straight Dope (a source I usually trust) has written an article about the controversy over microwave cooking, and he notes that scientists actually do not fully understand the chemical changes that take place when food is microwaved, and so there may indeed be some kind of "microwave effect." He notes a 1992 Stanford study that found microwaving breast milk mysteriously reduces its infection-fighting properties, as well as studies that have found that microwaves can accelerate certain chemical reactions. He writes: "'One suggestion,' a bunch of chemists wrote recently, 'is that this is some form of 'ponderomotive' driving force that arises when high frequency electric fields modulate ionic currents near interfaces with abrupt differences in ion mobility.'" He doesn't attempt to explain this theory.
I would repeat the girl's experiment myself, but everything I try to grow mysteriously dies, so there wouldn't be much point. (via The Greener Side)