Some people are saying it's a bear with a fish in its mouth. Since the resolution of most eyes is better than that of this video, that would mean that our vidographer is a liar, which is a possibility. I don't think it's a bear at all. In the zoomed-in (cropped and enlarged) you can see the suggestion of tusks. Not only that, if you look at the non-trunk part as a bear... well it doesn't look like a bear. It doesn't move like a bear.
My first thought was, "Why is it dragging its trunk in the water?" Elephants breathe through their trunks, I thought, so it should be holding it up. It turned out I was wrong.
Still, though, I don't believe that the first video is an actual mammoth. Is it because I'm a Polite Skeptic? Maybe. Is it because I don't think sightings of mammoths in Siberia are genuine? Well, they've only been dead 10,000 years, and stranger things have happened. There are two things, though, make me disbelieve the mammoth video.
1. Seems fake. This doesn't hold much weight in court, but it just seems fake. Its movements remind me more of bad animation than a breathing flesh-and-bone animal.
2. The vidographer's disinterest. It's the attitude of, "Whoa! Is that a mammoth! I will take a ten second video of it from a distance." I've taken longer videos of my kids blowing out their birthday candles. And he knows his camera isn't high quality, but he decided to record from the other side of the country.
All this, to me, seems like someone grabbed some nice footage of a creek, threw in a cgi mammoth, and then hit blur a few times.
If I wanted to fake a mammoth from a distance, I would throw together a costume not so different than Snuffy from Sesame Street. I'd get one guy for the back legs, and one for the front legs and head. Then, even from a distance, it could look pretty convincing, and have very natural movement that did, after all, come from an animal (the guy in front).
If it is a fake, it's a somewhat good one, and I'm sure this guy got his Reddit.com upvotes he was looking for.
edit 2018: It does look a lot like a bear to me now