So after having lived here a while and seen a variety of stuff catering to the tourist market (fun facts about Iceland and suchlike), a couple of things are particularly starting to stand out as bollocks.
Firstly, you may well have been told that there are "thirteen Santa Clauses" in Iceland. There are precisely no Santa Clauses in Iceland. What is interesting is that Iceland has maintained a rather different (although admittedly obviously related) folk tradition. The jólasveinar, or Yule Lads if you like, are indeed thirteen, and they do come and leave presents for children. But they do not live at the North Pole in a magical toy workshop staffed by elves or travel around on a magic sleigh pulled by flying reindeer, so not really sure why people would say that they are multiple Father Christmases. They are supposedly the mischievous sons of Grýla, a monstrous troll woman who lives in the mountains and carries off naughty children in a sack (although parents tend not to threaten their children in this manner these days). Each of the thirteen days leading up to Christmas, one of the Yule Lads comes down from the mountains and leaves a little present in children's shoes. This sounds like it must be an absolute pain for Icelandic parents, although probably no more a pain than doing a Christmas stocking. They all have names like Spoon-Licker and Door-Slammer and each is supposed to make mischief and trouble according to his name, although I don't think this features much in how people actually behave at Christmas, I think it's mostly about the presents. In the thirteen days after Christmas they leave again, one by one. Nowadays you will see people dressed in red and white with the beard and everything, who are supposed to be jólasveinar, and I think it's a bit sad that this old Icelandic folklore is being morphed into the Anglo-American traditions.
You may also have heard that Icelanders believe in elves. I won't lie, I was hoping that this would be true. But it really isn't, although it probably was in the 19th century. I have not met a single modern Icelander who professes to believe in elves. Of course there are mentallers in every country, so you can find a few in the media, but you'd probably find plenty of people in every country who believed in elves if you did some sort of survey. Elves are an interesting part of Icelandic folklore, but people don't really believe in folklore these days any more than we do in Britain. Incidentally, they are nothing like the Tolkien elves. They are just like normal, middle-class 19th-century (since that is when they first appeared in illustrations, that's the only reason) farming folk, except they are usually invisible and live in rocks.