How was Harry's scar useful as Dumbledore expected?

Question

‘He’ll have that scar for ever.’

‘Couldn’t you do something about it, Dumbledore?’ [said McGonagall]

‘Even if I could, I wouldn’t. Scars can come in useful. I have one myself above my left knee which is a perfect map of the London Underground. Well – give him here, Hagrid – we’d better get this over with.’
_{**Philosopher's Stone* - page 17 - Bloomsbury - chapter one, The Boy Who Lived}

I see Harry's scar as the spot where Voldemort's curse hit Harry, and a source of pain for him as the bit of Voldemort's soul sometimes attempts to exit Harry and rejoin its master.

How else is Harry's scar useful?

_{I'd prefer a canon-based answer (the books, J.K. Rowling interviews, Pottermore) but a subjective answer in the spirit of canon is perfectly fine.}

Answer 1

First off, the correct answer as to why Dumbledore said so is because he was pulling &^$% out of his behind, as usual. Note the weasel world "can". He had "guesses". Like, y'know, the scar is a product of deep scary magic and "Meant To Be".

---

However, to answer the question of how the scar was, indeed useful.

1. Most importantly, that scar is what enables Harry's mind to connect to Voldemort's - which is how Harry found out loads of relevant information in Deathly Hallows:

   First of all, a Word Of God:

   ... In choosing which boy to murder, he was also (without realising it) choosing which boy to anoint as the Chosen One – to give him tools no other wizard possessed – the scar and the ability it conferred, a magical window into Voldemort's mind (JKRowling.com FAQs, "What is the significance of Neville being the other boy to whom the prophecy might have referred?").

   Second, a collection of quotes from Deathly Hallows, to prove that the scar was indeed the mechanism for mental connection:

   “But it was supposed to have stopped! Your scar – it wasn’t supposed to do this anymore! You mustn’t let that connection open up again – Dumbledore wanted you to close your mind!”

   and

   Harry felt badgered, confused, and Hermione did not help as she said in a frightened voice, “Your scar, again? But what’s going on? I thought that connection had closed!”

   “It did, for a while,” muttered Harry; his scar was still painful, which made it hard to concentrate. “I – I think it’s started opening again whenever he loses control, that’s how it used to – ”

   and

   He wished that he had not told them what he had seen and felt; it made Voldemort more threatening, as though he were pressing against the window of the room, and still the pain in his scar was building and he fought it: It was like resisting the urge to be sick.

   and

   “I know it was your scar! I can tell by the look on your face! You were looking into Vol – ”

   and

   His scar burned, but he was master of the pain, he felt it, yet was apart from it. He had learned control at last, learned to shut his mind to Voldemort, the very thing Dumbledore had wanted him to learn from Snape.

   and

   The goblin looked slantwise at Harry, and the lightning scar on Harry’s forehead prickled, but he ignored it, refusing to acknowledge its pain or its invitation.

   and

   Judging by their worried looks, and by the continued pounding of his scar, his sudden excursion into Voldemort’s mind had not passed unnoticed

   The scar is mentioned anytime Harry sees into Voldemort's mind (Discussing Seven Potters fight with Ollivander, Looking for Gregorovitch, Rowle's punishment, finding Gregorovotch's former home, finding Gregorovitch, taking the Elder Wand from Dumbledore's tomb, finding missing Horcrux in the cave, etc...)

   Harry himself notes that he uses it to ferret out information:

   “Harry, you aren’t supposed to let this happen anymore!“ Hermione cried, her voice echoing through the bathroom. ”Dumbledore wanted you to use Occlumency! HE thought the connection was dangerous – Voldemort can use it, Harry! What good is it to watch him kill and torture, how can it help?“
   “Because it means I know what he’s doing,” said Harry.

   and

   Harry wished his scar would burn and show him Voldemort’s thoughts, because for the first time ever, he and Voldemort were united in wanting the very same thing

   and in the end in Hogwarts:

   “You need to find out where Voldemort is, because he’ll have the snake with him, won’t he? Do it, Harry – look inside him!”

   Why was it so easy? Because his scar had been burning for hours, yearning to show him Voldemort’s thoughts? He closed his eyes on her command, and at once, the screams and bangs and all the discordant sounds of the battle were drowned until they became distant, as though he stood far, far away from them…

   ---

2. It serves as tactical Voldemort detector, letting Harry know when Voldemort's dangerously near or approaching, warning him:

   . Harry raised his wand, but as he did so, his scar seared more painfully, more powerfully than it had done in years.
   “He’s coming! Hermione, he’s coming!” (DH, in Bathilda Bagshot's house)

   and

   then the scar on his forehead burned like fire: as a Death Eater appeared on either side of the bike, two Killing Curses missed Harry by millimeters, cast from behind – And then Harry saw him. Voldemort was flying like smoke on the wind, without broomstick or thestral to hold him, his snake-like face gleaming out of the blackness, his white fingers raising his wand again – (DH, Battle of Seven Potters)

   and

   “Good!” she leered. “Draco, pick them up! The Dark Lord is coming, Harry Potter! Your death approaches!”

   Harry knew it; his scar was bursting with the pain of it, and he could feel Voldemort flying through the sky from far away, over a dark and stormy sea, and soon he would be close enough to Apparate to them, and Harry could see no way out. (DH, Malfoy Manor)

   ... (same place) ... Harry’s scar was blinding him with pain. Dimly he knew that they had moments, seconds before Voldemort was with them.

   ---

3. It's a brand, an identity. Both for Harry AND for his supporters

   “Indeed they are, Romulus,” said Lee, “so we suggest that you continue to show your devotion to the man with the lightning scar by listening to Potterwatch! (DH)

   ---

4. Strategic "Is Voldemort still alive" detector

   The scar had not pained Harry for nineteen years. All was well. (DH, Epilogue)

Answer 2

I always thought that he meant it was useful as a reminder. Whenever he looks in the mirror he has a reminder of how much his mother loved him.

In the same way a scar on one's knee might function as a reminder that you are not invulnerable and to take care.

I have a scar on my forehead which reminds me to put my helmet on when I am sword fighting!

Answer 3

I also agree with Stefan, it’s a reminder, not just for Harry - but Dumbledore feels that it should be a reminder and a warning to all wizards who see that scar (or know about the scar).

Dumbledore is worried that memories of Voldemort and the terror he inspired, will become diluted, people will start believing (over time) that it is impossible for Voldemort to come back.

Dumbledore knows Voldemort will return somehow.

from Deathly Hollows chapter: The Prince’s Tale

while Harry was examining Snape’s memories in the Pensieve. This was the memory of events right after Lily’s death

“You know how and why she died. Make sure it was not in vain.

Help me protect Lily’s son.”

“He does not need protection. The Dark Lord has gone —”

“The Dark Lord will return, and Harry Potter will be in terrible danger when he does.”

Imagine going back to the time of Lily’s sacrifice

a few days after the news hits the newspapers, a good number of wizards might be 50 percent sure (in their mind) that Voldemort is dead.

a month later maybe 54 percent sure (in their mind) that Voldemort is dead

1 year later maybe 70 percent sure (in their mind) that Voldemort is dead

until many years later when uncertainty slides into certainty and many people think - 100 percent sure (in their mind) (that Voldemort is dead).

Goblet of Fire chapter Parting of ways

“See here, Dumbledore,” said Fudge, and Harry was astonished to see a slight smile dawning on his face, “you — you can’t seriously believe that. You-Know-Who — back? Come now, come now . . . certainly, Crouch may have believed himself to be acting upon You-Know-Who’s orders — but to take the word of a lunatic like that, Dumbledore . . .”

Fudge would have reacted differently if Voldemort came back a month after Lily’s death.

“don’t let your guard down” was Dumbledore’s message.

Dumbledore was hoping wizards will remember the fear and uncertainty they felt during the first days of Voldemort’s “supposed” death (if they see the scar or talk about Harry and his famous scar).

Of course wizards generally do not like to dwell on fear and uncertainty.