Slippery slope -- Asserting that if we allow A to happen, then Z will consequently happen too, therefore A should not happen.
Slippery slope is not necessarily a fallacy -- it is only a fallacy if the warrant is extreme. If we were arguing about dropping lit cigarette butts into the trash and we both agreed that fires were bad and I made the claim that we shouldn't drop cigarettes in the trash because they often cause fires (and cited data to that effect) there would be no fallacy in my argument.
Appeal to authority -- Using the opinion or position of an authority figure, or institution of authority, in place of an actual argument.
This one actually infuriates me because it may be the most wrongly used logical fallacy. First, because most people who use this argument are not making a logical deduction, they're making a statistical argument. To cite from Wikipedia:
The appeal to authority may take several forms. As a statistical syllogism, it will have the following basic structure:[1] Most of what authority a has to say on subject matter S is correct. a says p about S. Therefore, p is correct. The strength of this argument depends upon two factors:[1][2] The authority is a legitimate expert on the subject. A consensus exists among legitimate experts on the matter under discussion.
There is nothing wrong with this argument. The example given in the poster is very bad. As a PL student I have a bit of experience with formal methods and I'll remind everyone that the only things which can be proven using logic are those which follow directly from the definitions. In real arguments, these structures basically never exist. The truth never follows necessarily from the things people say, it's almost always a statistical argument. The fact that medical authorities used to think wrong things about the body didn't necessarily mean that it is or was wrong to believe in the body of scientific knowledge at the time. It only means that you have to be aware of the error margin in your statistics.