I don’t understand why the Predator shoots his spear when his helmet is off. Since they are laser-guided how does he know where they will go?
Video of the relevant scene (starts at 6:52):
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This bothered me as well. I can't add a comment to Paulie_D's answer, so in addition to that, my headcanon is that it is about range. The mask has to be close by for the targeting to work. Otherwise the arrows just fly straight.
The mud pit is not that close to the place where he lost the mask. He does not realize that Naru has carried the mask away and positioned it about two meters from where his head will be after she lures him into the pit. She doesn't need to know how to activate it, she understood what the red dots do, and she just needs a bit of luck.
Alternatively, the predator could be really stupid. He did not seem to understand how the targeting worked earlier in the movie, when he lost the mask for the first time. Maybe it was a gift, and he didn't read the instructions. Either works :-)
Out-of-universe, this is simply bad writing. The predators, or Yautja, are at least on par with humans when it comes to intelligence, so PaulieD's answer, that the predator doesn't realize the correlation between the helmet and a projectile's orbit, doesn't satisfy me. This specific predator already lost their helmet before, and they must have realised that their projectiles hit where they look (nicely indicated by those three dots they must necessarily see all the time) long before their HUD was unceremoniously removed - likely even before being dropped on Earth.
In-universe, vertigo jones's answer, that the alien is unaware of the close proximity of the helmet and concludes that manual targeting is activated, is a possibility, but I would like to add another option: anger. Their current prey has been eluding them this far, and managed to deeply wound them: they have been stabbed in several places, been shot in the back of the head, and lost an arm. This current prey keeps outsmarting them, even in close combat. It is certainly worth the trophy, but the humiliation clouds their judgement, and the predator just wants to get this over with, blindly shooting at a prey that is just out of physical reach.