First off I will say with all honesty, there is none, however I think this is something of a loaded question and really not so easy to give a definitive answer, I will attempt to address many of the common questions.
Why are the photos or videos shaky or blurred?
Well you have a couple of seconds to get a photo of something that just surprised you, how stable will you be?
Next you have to get that camera out, turn it on and then find the target. After fumbling around in my pack or pocket I end up losing the vast majority of decent pictures or even any picture of wild animals. Professionals make it look easy, but they spend hours upon hours and even days trying to get one good clear photo of an animal who's habits they are familiar with.
Up until the last decade taking pictures was a fairly complex task, you had to turn the camera on, bring it up and focus on your target. Those that did not require focus were fairly grainy anyhow. Think back to your old family photos, how many heads were cut off? people on the left or right? it seemed nearly impossible to get proper photos, and these are people standing perfectly still.
Further most Cameras lack a decent zoom on them, that is changing now, however up until the last couple of years you were stuck with minute zooms, how well do you really think you would get a picture of an animal several hundred yards away? Probably not at all and especially nothing identifiable.
Now with modern technology it is easier to a point, however auto focus still tends to focus on that branch in front of you and not the target behind. Lets say you have that camera out, now you still are left with the problem of the creature behind the bush and are screwed, not to mention at this point anyone with a legitimate sighting is scared out of their wits and wants to go home :P
Shaky video makes sense as well, ask any hunter how bad he shook at the first deer he shot at and he will tell you he was shaking like a leaf. Hell Elk still make me nervous as hell, buck fever does come into play.
There is also the inevitable of people do not know what the hell they are looking at, sadly this is true. If we watch break downs of photos or videos despite logical explanations as to what is actually being seen, people simply will argue that they are indeed seeing Bigfoot when in reality, all they are seeing is some sort of a fake or miss identification.
This is not limited only to Bigfoot or UFOs, people fabricate in their minds as well which is why eye witness testimony is notably unreliable in court.
Hell I lost count of how many hours I spent in the woods, and I still see something in the distance at times that makes me look twice, and that was before I ever had my sighting. Since then little has changed, in the back of my mind I know it was a one in a billion thing, I hope, but I know I probably will never see anything like that again. SO that black stump in the distance is usually exactly that, a black stump and I do not assume otherwise and I always will remain skeptical using Occams Razor theory, the simplest explanation is usually the proper one.
What about tracks?
Well sadly most people have no Idea what they are actually looking at, bear tracks actually look very similar to human tracks, which is why they are often cast.
Trail Cams are becoming popular, between them and Drones at some point a legitimate picture will be taken and from there hopefully physical evidence will be gathered and found.
The Physical Evidence really needs to be done by professionals as the common person does not know what they are looking at or how to properly gather the evidence. This is also why the recent DNA gathering has turned up nothing more than common known species, such as horse, bear, dog etc.
Overall please stay skeptical, falling for hoaxes does nothing more than encourage more hoaxers and decrease the odds of science ever taking it credible as it is, and it already is next to Impossible.
This also does not take into account the hundreds of photos and video taken by people who had their one weekend in a lifetime out in the woods at a well traveled campground, but hey, they KNOW what they saw! *wink*
Only a handful of scientists actually still believe in it, one of the most famous being Jane Goodall who holds out hope to this day.
Sadly without science actively getting involved little more will come of this until some hunter manages to actually bag one.
I hope science takes a hard look at this, however if they do not, I completely understand.