I think it would have to be "Heroes never make mistakes" because there are numerous examples in The Iliad when they do indeed make mistakes. Heroes, though exceptional in many ways, are nonetheless human, and as humans they inevitably make mistakes.
Agamemnon, for example, could be described as a hero; not in the same vein as Achilles, perhaps, but a hero all the same time. At the very least, he lives by an ancient heroic warrior code. Agamemnon makes a serious mistake in depriving Achilles of his war booty, the sex slave Briseis, she of the lovely cheeks. This sends Achilles off into a major sulk, brooding in his tent while his comrades get slaughtered on the battlefield in increasing numbers. To his credit, Agamemnon realizes his mistake and tries to make it up to his most feared warrior. But Achilles isn't interested. He'll only return to the fray when his close friend and comrade Patroclus is slain in battle by Hector, breaker of horses.
Hector is also a hero, and he too makes many serious mistakes. For one thing, he makes a rash promise to the Trojans that they will definitely defeat the Achaeans. He's been brought to this erroneous conclusion by his opponents' sudden withdrawal back to their ships. Hector doesn't seem to realize that this is all part of Zeus's grand plan, and has nothing to do with any exceptional military prowess he may possess.
Hector's misreading of the situation leads him to make another mistake, this time electing to keep his troops where they are, occupying the plain, instead of making a tactical retreat to the city as another Trojan hero, Polydamas, sagely advises. In this example, we can see that living up to an heroic code and making mistakes often go hand in hand. Hector won't retreat to Troy because that would be dishonorable, completely unheroic. As far as he's concerned, the Trojans have their opponents on the run, and so it would be ignoble for them not to press home their advantage. Hector, as with Agamemnon on the other side, is so blinded by a lust for glory, so obsessed with conforming to the ideal of what a hero should be, that he's not prepared to listen to reason until it's too late.