The mermaid is mummified monkey's head and torso sewn on to a stuffed fish. They were popular sideshow attractions in the 1800's. Creepy as heck, but fake.
I'm pretty skeptical when it comes to a lot of stuff, but I don't like when things are dismissed out of hand - the best scientists of the day once swore black and blue the earth was flat, you know? There's always something we don't know about and/or don't believe in lurking around somewhere, waiting for science to make it valid.
I do think a few remnant dinosaur-age creatures might have survived in the sea or in deep forest somewhere. The coelecanth was thought to be extinct for millions of years, until somebody caught one in a net. Same for humanoids - a very sane Aussie guy I know saw a yowie (our version of Bigfoot) and has spent many years since trying to track them down. He's not an idiot, and I do believe he saw something like a yowie out there in the bush.
Almost every nation on earth has legends of white 'dragons' or 'serpent-people', who gave humans advanced knowledge, interbred with humans, and possessed 'magic' - pretty much the same stories as told about the 'faery folk' (not the little one, the big scary ones). It's very curious to me that this story is almost exactly the same or at least has major points in common all over the world. I'm not sure what to make of it, but I think our myths of 'dragon-people' very well may have had a source in some adventurous, advanced humanoid race which existed in the dawn of our own time. But I take the wild descriptions with a grain of salt - centaurs were created by the Greeks when they needed to explain the Scythians, the most powerful horse-riding, nomadic warrior race ever. Maye these human-like 'dragons' were associated with reptiles in some way and came to be thought of as part-reptile, as the Scythians were depicted as half-horses.
I do believe in elemental spirits (the little fairies) but not that they are necessarily humanoid. I also believe there may be multiple dimensions, some of them overlapping our own, and the majority of which we can't percieve in general via our limited range of perception.
Phew. tl;dr version: I'm not sure about mythical beings. But I can't discount them entirely.