Okay, so this time we have a lovely little story from the clergyman, based around those eeevil pagan religions. It's always a bit weird to look back on times when "the enlightened civilization" was uber-Christian, and anything different was just evil and/or uneducated.
Anyhow, I think this story's a bit over-the-top with the atmosphere and pagan symbols, but it also helps to mask a neat little "whodunnit and how" mystery, so that balances out. It misdirects the audience (both reading and in the book) fairly well with all the trappings and the idea of "*gasp* the weapon VANISHED! And the second victim is still alive and his story makes it even MORE mysterious!" and deftly causes us to ignore the very simple direct explanation. Especially with the larger, more varied cast to allow for more possibilities.
That said, I'm not completely convinced that no one would look down and say "oh hey, you have a huge honking knife RIGHT ON YOU, let's at least check this out, 'kay?" but... it's just plausible enough that I guess it can get a pass for the sake of the story.
Also, the setting of this story reminds me of the Hound of the Baskervilles, with the moor-like setting, the relics, and the tors (that novel is the first place I saw that word). The murder-mystery aura doesn't hurt the comparison, either.
As a final note, it's a bit... not odd, perhaps, but definitely a mark of the past that various people that are supposed to be out of touch with society for a long while (and possibly gotten rid of cleanly, such as in this case) are shipped off to the poles. Such as Frankenstein, the murderer here, and a main character in at least one other Christie book that I can think of. These days, while people aren't exactly jaunting over to the South Pole for a week's holiday, the Poles definitely don't still have that aura of impenetrability and extreme danger that, from reading, they used to.
Anyhow... have at it!