I just want to understand WHY brain cells .... are okay with aneuploidy
Great question. The standard hypothesis has been that aneuploidy confers some kind of advantage to the function of the organ (brain). After initial reports estimated a very high (>30% of brain cells) aneuploidy, it would be plausible that any potential negative effect would somehow have to be compensated. One hypothesis was that it increases the functional diversity of the neurons.
However, this notion is outdated. For instance, a recent study, which also nicely summarizes preceding literature, and has been published by Knouse et al. PNAS 2014 ( http://www.pnas.org/content/111/37/13409.full ), and has applied a more sensitive and accurate measurement, and also surveyed other tissues, found that the fraction of aneuploid cells in the brain is around 1-2%, and not higher than in most other tissues. One possible conclusion, which has also been drawn by the authors, is that for the brain aneuploidy is as much of a problem as for other organs, and that - given the low fraction of aneuploid cells, which is similar to other tissues - aneuploid cells in the brain do not contribute to some special organ-specific property. (Concerning your related questions to brain: the aneuploidy in brain is believed to result from cell division artifacts - also see paper mentioned above.)
I just want to understand WHY ... plant cells are okay with aneuploidy
Although plants appear more tolerant against aneuploidy than humans, aneuploidy can be quite harmful to them, and can easily lead to phenotypic aberrations. While the basis of the increased resistance of plants over humans isn't known, or at least hasn't been known at the time of the publication listed below, it appears linked to some genetic factors as different strains can have a different robustness - see Henry et al. , Genetics, 2010 ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2998307/ )
Is aneuploidy/aneusomy only a problem for cell division?
No, aneuploidy can create further problems (e.g.: also see second paper). For instance, in plants, it can also change the activity of genes, or the spatial organization of chromosomes - as described in Huettel et al. Plos Genetics, 2008 ( http://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1000226 )