I think the fact that the author is a homeopath should be a warning sign, but you cannot dismiss the study simply because it was done by a homeopath. Ultimately, it is the quality of the study, not the credentials of the author, that determine its validity.
I'm sure people can spot a dozen different red flags with this so-called study, but regarding the quality of research I thought I'd point this one out:
"Eighty-one families had both vaccinated and unvaccinated children. The vast majority of these were two child families in which the elder child was vaccinated and the younger unvaccinated. There were also a large number of three and four child families in which the youngest child was unvaccinated and the older siblings were vaccinated."
Great! That data will be somewhat useful at reducing parental bias in reporting ailments. I scrolled down to the results section to find .... nothing. No graph, table, or even a mention of single-family results. The best evidence that could have been given, and would have taken very little effort to analyze, was not reported. It wouldn't even surprise me if there was still a noticeable difference with those families (they could have changed other parenting habits with their youngest child), but why on earth wouldn't you publish that data?