In that 866 page report the researchers analyze a great breadth of data and research on connections between vaccines and all sorts of nasty things. And one phrase you might find worth ctrl+fing is "The evidence is inadequate to accept or reject a causal relationship between". You'll find it repeated constantly throughout the report as the academy researchers come to their conclusion on the validity (or lack thereof) of a causal link between vaccines and all sorts of nasty stuff. And for many of these nasty correlations while the evidence is insufficient claim a causal link, it's also insufficient to reject it. Not exactly what you'd call settled science.
Of course this does not justify turning against vaccinations. Even if there is a causal link found between vaccines and some of these various issues, the possibility of significant numbers of people choosing to not vaccinate would be catastrophic. For instance we're right now on the cusp of completely eliminating polio, much as we did smallpox. In fact you are currently more likely to get polio from a vaccine than in the wild. And some people might use that as a reason to stop vaccinating. But if they did, that would rapidly change. The one and only thing that's bringing us to where we are is people choosing to vaccinate. So it comes down to a matter of social responsibility. Vaccines are not without risk but whatever risk there is greatly outweighed by the collective benefits.
http://nationalacademies.org/HMD/Reports/2011/Adverse-Effect...
New vaccines are created and may have side effects. E.g. H1N1 vaccine causing narcolepsy in Europe recently: https://www.cdc.gov/vaccinesafety/concerns/history/narcoleps...
Using the phrase "the science is settled" is silly, given that the creation and manufacturing of new vaccines isn't settled.
Let's say I'm someone that really hates vaccines. I begin spreading rumors throughout the internet that vaccines cause cancer. My evidence? Most of the people that have cancer had vaccines at one point in the past.
Now how does science disprove this? Through years of study, research and data collection over many decades. Even then, it would be hard to accept or reject a casual relationship between cancer and vaccines, because that is an almost endless set of data. All I would have to do is make up some new casual correlation between vaccines and Y as an attack vector. This is exactly how arguments against climate change are made as well. Science is never really settled, but we can reach a high level of confidence on how something works.
Worse, because of the way confidence intervals work, if you generate enough bad hypotheses and run experiments, eventually you find one where it appears to be true!