Slippery slope is a logical fallacy that occurs when one unjustly argues that if one event happens, others will follow. If one event happens and one argues that others will follow, he/she has to show that there is a logical link from one event to another, but this often is not the case. This argument is very common in the gay marriage debate - opponents of gay marriage often argue that if gay marriage is legal, people will soon be able to marry their close family members and animals.
Around 1:20, Ron Paul commits the slippery slope fallacy and argues that if we don't have the right to "do things that are controversial," the government will tell us what we can "eat and drink and whatever." The phrase "things that are controversial" is very vague, but to be charitable, Paul only had a short moment to elaborate on this phase and this is a soundbyte. A government that tells as what we can eat and drink simply doesn't follow from the loss of the ability to "do things that are controversial." Imagine if the Supreme Court, for example, made flag burning or protesting funerals illegal - government restrictions on food and drink would not automatically follow. Government banning would be an entirely separate issue and so would the government telling us what to eat and drink.
In order to argue that loss of liberty or the government telling people what to eat and drink would follow from stopping people from doing controversial things, the arguer would have to make an entirely different case. The government can stop us from legally engaging in "controversial things" and already has (prostitution, polygamy, vicious beating of children in schools, sodomy ( this is controversial to some)), but loss of liberty in the area of food and drink did not follow.