I've heard the claim that legalizing gay marriage would lead to legalizing incestuous marriage. I strenuously doubt that it would lead to an actual conscious choice to do so. The arguments against incestuous relationships (that they are likely to be abusive due to power dynamics and the inability to separate families via devorce) are totally separate from the arguments against gay relationships (I cannot actually think of any non-specious ones)
It is amusing to note that Massachusetts, has a law making it illegal to marry your sibling, parent, child, etc. so long as they are the opposite gender as you. When in 2004 gay marriage became legal, the law this failed to prohibit same-sex marriage between blood relatives. This wasn't a policy decision by anyone: The legislature simply failed to update the code.
(Not claiming marriage equality would lead to plural marriage; just surprising how seldom it's brought up, relative to nonsense about marrying dogs.)
Legally-recognized polyamorous relationships, in one form or another, is probably going to be the next evolution of marriage laws, and there's a bit of discussion about it, but it won't get much attention until it bubbles up to the top of the queue. That might take on the order of years or decades to happen.
Whereas, "sure collect everyone's correspondences, but delete people who are citizens" isn't a far jump to "ok, you don't really need to delete anything".
The wikipedia article is a very good summary of the phenomenon and the several factors that have a role in creating it.
IMHO there is no more certain indication that someone has been educated beyond their intelligence than when they sign onto an Internet forum and start braying about how the slippery-slope argument is a "logical fallacy." While technically correct, they betray an ignorance of how human beings -- a decidedly non-logical species -- actually behave.