First - how in the world did you end up in this sub, if you aren't adding comments here as a job? You seem to very pro-authoritarian and very trusting of governments! Once your shift is over, I encourage you to go read up on governments - any of them really. At best, they trample the rights and liberties of its' citizens; at worst, they kill millions of their own people. With that said, it's alarming that you have so much trust and see a government as some benevolent force for the people. To have that viewpoint without any reason or evidence of why - is the much more alarming thing!
Second - this is a predictable response. The "go to" thing is: "but how will we moderate civil disputes?". Yes, most everyone agrees there needs to an unbiased 3rd party to moderate what is reasonable. THAT, is not what a government is. A government is a body who makes decisions without your input, and then uses threat-of-force to make sure you do it.
Lastly, you make it sound like vaccines are a "proven science" without any downside. Knowing now that you don't seem to be a critical thinker, I want to provide sources that you will likely read - here is a start from yahoo answers, which cites several examples of vaccines causing harm or killing people.
As for a slippery slope, I hear what you are saying - but on the other hand, there is no other reasonable, rational alternative. Knowing human nature and our political system, I would argue it is 100.0000% impossible that we could have a law on the books that requires mandatory vaccination (a law, requiring citizens to buy something) and it not be exploited for financial gain in the future (and/or be expanded). There is no scenario where it is reasonable that this law wouldn't be used to "guarantee" that other companies or other industries get sales from the citizens mandated.
Oh, and lastly - you are also forgetting the golden rule of Authoritarianism: whatever you get you passed for your ideals, also applies to your enemies. Remember the people who wanted to get rid of presidential term limits for Bill Clinton, so he could keep running for president? That would mean that those term limits would also be gone for G.W. Bush too. Likewise, if they make a law that mandates a drug you like, now - that also means they could mandate a drug you don't like. Therefore, when you make a law that really let's you exploit people or makes them bend to your will - you need to ask yourself: "What if my nemesis also had this power?".