Apologies if some of this ground has been covered.
There was a post like this made on another forum, but since I can't re-post the content, I'm posting a new version. The examples shown here can apply to any cryptid, not just Bigfoot.
Top 5 Skeptical Fallacies
1) Appeal to Ignorance
"After thousands of years of being on the continent, we would have had proof of Bigfoot by now if Bigfoot was real."
This is a fallacy where something is considered to be false either because it hasn't been proven to be true or because it's just hard to believe that it could be true. It's not possible to know about something you haven't discovered yet, so it doesn't make sense to conclude that something isn't real, simply because it hasn't been discovered.
It depends on how much (and how well) you've searched. If the police have torn a house apart looking for a murder weapon, and can't find it, there's a good chance it's not there. That's a correct conclusion to make.
In the case of alien life, it's absurd to conclude it doesn't exist just because we haven't found any evidence. If we eventually search 99% of the galaxy, and can't find it, then yeah, you could assert it's probably not in the 1% we haven't looked at. But we've examined only a tiny sliver of galaxy so far.
So in the case of Bigfoot, have we done a good search for it? Is there an expectation that if one existed it (or its remains) should have been found by now? Yes. It would be very surprising to discover an intelligent large humanoid creature living in the forest that's really adept at not being spotted, filmed, photographed, and apparently leaves no trace of itself when it dies.
2) Argumentum Ad Populum
"The current consensus is that Bigfoot isn't a real animal, therefore it isn't real and isn't worthy of scientific investigation."
A fallacious argument where it's concluded that a proposition is true because many or most people believe it.
Again, it depends. Sometimes it's perfectly valid in informal logic, which is what goes on in these discussions. If 99% of climate scientists claim X, then that carries a lot of weight. The person appealing to the 1% that claim Not-X has a much higher hill to climb to prove their position.
The reason is that when 99% of experts agree on something in their field of expertise, they're usually right. Not all the time, but for every Pasteur that comes along and overturns the consensus position, there's a million crackpots who've advanced competing theories and utterly failed.
If your position is supported by a large number of experts, you're in a good spot, epistemologically speaking.
3) Burden of Proof and False Default Position
"Bigfoot doesn't exist and it's up to proponents to prove otherwise."
The denialist assumes a negative default position and shifts the burden of proof to others.
It's not possible to prove a negative in the case of Bigfoot, so the burden of proof in this case can't ever be fulfilled. It's important to at least be theoretically able to back up the claims you make.
The burden of proof is always on the person going against what the consensus position of the experts is, for the reasons I already gave: the reason a consensus exists is because a lot of smart people have looked at the evidence, and come to the same conclusion. To go against the consensus is to assert that you're seeing something that a whole lot of experts aren't seeing, or that they're all making some mistake, or ignoring some vital evidence. It happens in science, but not that often.
4) Special Pleading
"No other film like the PGF has surfaced since 1967, therefore, the PGF isn't evidence for the existence of Bigfoot." or "The film doesn't qualify as evidence."
Moving the goalpost after the claim of there not being any evidence has been shown to be false.
Or a claim that Big Foot skeletons don't exist because they rapidly disintegrate after death. Or Big Foot (feet, what the hell is the plural?) has psychic powers that alert them when they're being observed or filmed.
5) Genetic
"The PGF was made by a person with a questionable history, therefore, the film itself should be dismissed."
This fallacy avoids the argument by shifting focus onto something or someone's origins. It's similar to an ad hominem fallacy in that the skeptic leverages existing negative perceptions to make the PGF look bad, without actually presenting a case for why the film itself lacks merit.
Yeah that's a fallacy, but it's usually done to save time, and if you do it correctly, you can usually get away with it. For example, I generally don't believe anyone who sources wattsupwiththat.com (climate denial website), and in doing that I'm pretty safe, but I imagine they might get something right every once and awhile.