PDF source:
http://thechifarm.com/wp-content/uploads/2013/10/am-j-clin-nutr-2010-urashima-1255-60.pdf
Some obvious problems are the children being hospital outpatients (therefore more likely to be vitamin D deficient), a fair amount of difference between drop out rates when comparing vitamin D participants to placebo participants, and the numbers not being 99% significant (except for asthma, where they were 99.999% significant - however, that does concern me a little, maybe I'm missing something, but they state 56% of children over the age of 3 (why did they state that when making it greater or equal to in the table?) had asthma, whereas I make it 110 out of 282, so 39% - I'd like to see a more complete breakdown of ages etc to see where that discrepancy's coming from) - however, 97.8% significance is respectable.
Obviously, as they stated, it was on children, so may or may not be applicable to adults. I'm also not sure why they didn't test initially for vitamin D levels, that's a pretty important thing to know, and not hard to do. Overall though, seems fairly good as an initial study, I may be wrong though, I'm no scientist. I'm sure someone else who is will be able to chip in.