The Federalist has published a very good article by Ian Haworth that tackles the 10 most articulated points made by critics or opponents of vaccines by answering them with facts. In the beginning of his essay Haworth correctly points out:
People who reject vaccinations for preventable, deadly diseases are driving a new and dangerous wave of misinformation. This is causing a reduction in vaccination rates, leading to outbreaks of diseases such as measles across the country. We must combat this small but incredibly vocal minority, and use scientific objectivity to prevent them from driving vaccination rates further downwards.
You can read his breakdown of the 10 most used arguments against vaccines here.
Unfortunately, the most important point left out of the entire debate about vaccines is the ideological underpinnings of the groups behind the opposition to or criticism of them. This is important to understanding not just vaccine opponents, but also to stop the spread of misinformation or outright lies about vaccines.
The modern day anti-vaccine movement is an environmentalist front that seeks to eradicate humans by infecting people with diseases (like measles or small pox) so people can die slow, painful deaths. Undermining vaccines by lying or spreading falsehoods about them will help accomplish this goal a lot faster.