Prophets among Men are interesting, no matter what the story
If they were Hebrew prophets, they would be speaking the words of God (Eru himself) with the purpose of admonishing or giving hope. The outcome could be changed (sometimes) if the behavior of the people changed. If they were Greek oracles, they would be speaking on behalf of the gods (and trying to get around what they say merely brings it about, of course). There is a destiny, or inevitable doom, about such words. You
will be killed by your daughter's son. Deal. If they're Tolkienian (but non-Middle Earth), they are likely struck with sudden inspiration (Lo!) - poets. If they are elves, their hearts are likely in tune with the music and any such pronouncement will prove true.
But if they are Men of Númenor, who have the blood of Lúthien in their veins.....
Malbeth the Seer names Arvedui with some, but not all, knowledge of what will happen. He realizes that a choice will come before the Numenoreans, and that they will have to take the less promising one to survive. He does not know which choice they will make! But he guesses which course is more likely (the more obvious, hopeful one). It is unclear whether or not he knows the decision in question is the succession in Gondor, but he
does know the consequence will be the end of the North Kingdom (Arvedui means "last king"). This is partial knowledge, not full knowledge, and has some of the riddling of the Greek oracles in it. It isn't a "three days and Nineveh will be destroyed" prophecy. But what it does share with Jonah's is that there is the possibility that it
won't come true. He sees only the moment of decision, not the actual decision. But like Simeon, Malbeth is given a vision of hope to go with his vision of doom. He may know (or "see") the end of the North Kingdom, but the poem about
athelas speaks of a King's hands. [I am sure there are Northern examples I could be using for comparison; I am simply not familiar with them.]
Aragorn tells Gandalf to beware passing the gates of Moria, and, lo and behold, Gandalf dies there. Aragorn had a foreboding for Gandalf in particular (not the rest of the company), though he had no way of knowing about the Balrog. He and Gandalf had each (separately) entered Moria before, so they should have known what the dangers were. But it isn't a calculated risk analysis Aragorn is presenting, it's a "my heart tells me" you're screwed.
He also tells Éomer they will meet again, "though all the forces of Mordor lie between us." They meet in the midst of the Pelennor during the battle, so, again, Aragorn was right. What seems to be happening is that he has "glimpses" of what will be. He certainly
intended to make it to that battle and be reunited with Éomer, but either of them could have died first. He didn't say it to Théoden, after all.
There are only two "mistakes" in prophesying that I know of. Elrond's heart is against Merry and Pippin going with the Fellowship, and in particular, he speaks against Pippin going. Why? I think he fears for the little guys, but he also seems to have a 'glimpse' of doom. (Though he [and Galadriel?] admit that all foretelling is vain with such darkness covering everything). In reality, this foreboding may be left-over from a version in which Pippin would die at the Black Gate. But it was left in, presumably for a reason. Also, Frodo gets the order of Sam's kids wrong - Merry and Pippin are next to each other in age, and Goldilocks is younger. (Or something - I don't have the family trees in front of me.) I am not counting Saruman's threat that the Shire will wither if he is struck down there, because it was just that - an empty threat.
Conditional prophesying is interesting as well. Galadriel tells Gimli that
if he makes it through the war, his fingers will run with gold, though gold will have no power over him. In the current story, (see, I'm on topic!) Gwindor warns Túrin that
if he fails Finduilas, his doom will find him. Suggesting that it
was possible for him to escape the full doom Morgoth plotted if he had managed to rescue Finduilas.... I certainly see how she could have been protection against marrying Neinor! But who is the match for a dragon's riddling words? (Other than Bilbo, of course

) And if the Black Sword had done what the Men of Brethil attempted, how would it have been any different? Wouldn't Finduilas merely have been killed before his eyes, rather than in his absense? So, maybe Túrin couldn't help but fail Finduilas, no matter what he did..... Conditional prophecies are quite tricksy

.
But if we are speaking of Mandos - anything he says is true. He is the truest-speaking Vala. In other words, he is unlikely to make mistakes, because if he does not know, he keeps his mouth shut

. The question now is, did he ever make such a prophesy, or was one merely attributed to him? I think it funny to label it "merely myth" when the same can (and should) be said of the Ainulindalie and Valaquenta. Everyone is quite comfortable with the world being sung into existence (through the Ainur) and the names and characters of the Valar as laid out at the beginning. Why a sudden moment of doubt and clamor for "real" history at the end of the story? A decent cosmology should have a beginning and an end (as well as an explanation of the purpose in traveling between the two). All of Tolkien's work points to an end to the story. Something apocolyptic is always mythic, but this doesn't make it any less true. Whether the story is described as philosophic conjecture or a prophesy, it can still be true. Finrod hits near the mark in the Athrabeth, does he not? He postulates the need for Eru to enter into Arda to heal it, though he does not see how this could be. He also says that when it is remade, elves and men will have different roles, and states what they will (or may) be - I think he's telling the truth! He may be wrong in the details, but he understands the story too well to have missed the point entirely. If we can accept his thoughts, why can we not accept Mannish myths? Are they so far off the mark?