The boar's tusk helmet is the only one, in a tacked-on bit that was inserted into the epic. That's why it's well known. There's tons of material that doesn't match contemporary Greece, such as the extreme rarity of iron and the lack of writing, but it can all be read as false archaism.

False archaism is a specific kind of anachronism. It's when you want your story to seem old, so you stick in random old elements regardless of whether they have anything to do with the setting. The result is a hodge-podge. False archaisms aren't records of a bygone era, they're there to give an atmosphere, a flavour of archaic-ness. Some well known examples are the woad in Robin Hood: Prince of Thieves and Braveheart (supposedly set ca. 1190 and 1297, making the woad at least a thousand years out of place), or references to Roman gods in King Lear (supposedly set in pre-Roman Britain).

In the case of the rarity of iron, iron was just starting to see widespread use in 1200 BCE, and Greeks of Homer's time were aware that iron smelting was difficult and a comparatively recent technology. So Homer depicts iron as a rare, prized metal. It's a prestige item. At one point Achilles makes a hunk of unrefined pig-iron a prize in an athletic contest (Iliad 23.826-835). Except iron was never a prestige item. Even in Achilles' description of the iron, he outlines uses for it as follows:

Even if the winner’s rich flocks are very far away,
it will last him for a full five years
using it: his shepherd won’t need to go to the city in want of iron,
nor his ploughman. This will provide it.

This is not a prestige item! We have a mismatch between the iron's supposed value and its actual function, and that's a dead giveaway that we're looking at a case of false archaism.

This is typical of how Homer depicts old things. There's a flavour of archaism (long ago, people weren't able to produce iron as easily as they can nowadays), but no context: it's all out of place.

This applies to many, many aspects of Homer. The Cyclopes in Odyssey 9 sound a little like Neolithic hunter-gatherers, but their society is designed as something lacking all characteristics of contemporary Greek culture, not a description of characteristics that are present. Hence, false archaism. The same goes for the relationship between gift-exchange and trade: gift-exchange is supposedly a prehistoric counterpart to 7th century BCE trade, but the Odyssey depicts trade and gift-exchange going on alongside each other. The use of chariots in the Iliad, as a 'taxi service' for infantry, is an archaic elements (chariots) injected into a contemporary military practice (the use of mounted infantry on horses, not chariots).

Does it sound like I’m suggesting we should be looking for false archaism behind every bush in Homer? If so, that’s good, because that's exactly the message I'm trying to send.

No use of writing in Homer? May well be false archaism.

The position of basileus sounds less like a king and more like a 'big man'? May well be false archaism.

No hoplites or phalanxes? May well be false archaism.

Narrative poetry is sung, not recited? May well be false archaism.

In the case of the boar's tusk helmet, it's best to adopt the same approach. We're not looking at a Mycenaean artefact in its proper historical context, we're looking at an archaic element injected into a story to make the story seem old. In the past some scholars have tried to make similar claims about Aias' shield, claiming that it's a Mycenaean tower shield, except it obviously isn't: it's most simply read as a 7th century round aspis, and its unusualness is the fact that Aias is so strong that he can wield a gigantic aspis that reaches from his chin to his feet (Van Wees covers this in his piece in Greece & Rome 1994).

There are only two other elements of the Iliad where we can be certain they originated in a Bronze Age context.

1. There are references to a handful of towns which were abandoned at the time the Iliad was composed and not resettled until later, and one, the Boeotian town of Eutreus (as it appears in Linear B: TH Ft 140) or Eutresis (Iliad 2.502), had been abandoned around 1200 BCE. That's the most archaic case of a reference to an abandoned settlement.

2. There's one word that gets used in a sense that hadn’t existed since the Bronze Age, anax 'king' (Mycenaean wa-na-ka), which gets used regularly for the Greek leader Agamemnon (king of either Argos or Mycenae depending on which bit of the Iliad you’re looking at).

But anax, too, is false archaism: the word anax isn't a fact about Agamemnon that had been remembered for centuries, it's almost certainly a borrowing from Adrestus, anax of Argos in the Thebaid (and that would also be how the confusion with Argos arose).

The overall upshot depends on how you want to swing it. On the one hand, you can emphasise that Homer genuinely does stick in some elements that are genuinely archaic. On the other hand, you can emphasise that they're always wildly misrepresented. Homer isn't representing Bronze Age Greece or even 10th century Greece, he's depicting 8th-7th century Greece drenched in false archaism; but even false archaism has something archaic about it.

Note: I borrowed some examples and language from a write-up I did a few years ago, which talks about many of them in much greater detail.