I’ve been looking around for studies that injected children with placebo or vaccine randomly, and study their health (not just whether they got some specific disease supposed to be prevented). The one I discussed in the last post on confirmation bias is actually the only one I have found that tracked kids for more than 4 months. I haven’t looked incredibly hard, but if anybody knows of others please let me know. Right now the only placebo study of a vaccine of which I am cognizant that injected kids and tracked them for more than 4 months reported the vaccine was hugely damaging to their immune systems.
http://www.ncbi.nlm.nih.gov/pubmed/22423139

As an aside: its more common to see studies that use another vaccine instead of a placebo!
As another aside: the only study I know that fed animals GMO’s and tracked them for more than 3 months found lots of cancer.

In the search, I came upon another (non-placebo) study that claimed that injecting pregnant women with flu vaccine made their infants when born less likely to be hospitalized for flu. They studied this by looking at why hospitalized infants were hospitalized and finding a smaller fraction of the time it was for flu if the mother was vaccinated than otherwise. Unfortunately, they didn’t comment on the fact that their data were at least equally explainable by assuming the children of the vaccinated mothers got sick more rather than got the flu less. Pure confirmation bias to assume one and ignore the other. I’d bet on the damage rather than the protection.

http://www.ncbi.nlm.nih.gov/pubmed/21058908

Correction: I previously critiqued another study on TDaP but think I misunderstood how it was done.
Looking at it again it seems all right.