Why is Teddy Daniels wearing a band-aid above his left eye?

I'm still digging for better sources (specifically something directly quoting Marin Scorsese), but from what I've found so far: The bandage was very much intentional and used to symbolize Teddy Daniels'/ Andrew Laeddis' fractured psyche and amnesia.

Taken from http://imatrix.wikia.com/wiki/Shutter_Island

Martin Scorsese is notorious for bringing in patterns to his work of art. In his most recent movie, Hugo, the clock was a fairly significant symbol that appeared frequently. Scorsese wanted to have some sort of symbol to play a role in determining if Teddy was in reality or not. For this movie, the bandage on DiCacprio's forehead gives it away. Only the most observing type of viewer can figure out and come to a conclusion that Scorsese had in mind.

Whenever Teddy is pretending to be a U.S. Marshal, he had a bandaid on the left part of his forehead. Almost as if a wound. Teddy has a band aid on his head to represent him having amnesia and constant headaches. In one scene a doctor of the institute calms Teddy down and tells him that he truly is wounded. Wounds come from memories, tragedies, and dreams: all of which he possesses. He then hates the fact that he has been told something he does not want to hear and then foregoes to harm the doctor. The wound did in fact make him into a monster. Throughout the entire movie , whenever he has a bandaid on his head, he is running from his reality, and continuing his wish of make believe.

Any time we see the bandage gone is when Teddy/Andrew realizes the truth and is having a moment of clarity.

The bandage is removed from DiCaprio's head for the scenes where he is no longer lost in his make believe plot. Whether it be in a flashback of when he was in the war or to the day his wife drowned his children, the bandage is not present. This is the same moment in the film when everything descends into madness. It’s a simple yet really effective device. The scene analyzed above is one famous scene in which his bandage is missing. Why? Because Dr. John Cawley finally gives up and tells him his reality. Teddy has been living in his lie for so long that he is nearly able to completely convince himself of that reality. Because Martin Scorsese has a very creative mind and wants to challenge the viewers of his movies, he is able to capture the whole film with this ongoing symbol that truly tells it all. No one ever really notices it until it is pointed out.

Taken from an interview with Marin Scorsese about Shutter Island (emphasis: mine):

The film has a major twist at the end. Up until then, it’s something of a shaggy-dog story, keeping us hanging to the end.

‘But that’s life, isn’t it [another loud laugh]? It may very well be life, for all we know. I don’t mean to be sitting here being so glibly “philosophical”, but as you get older… What is? And who is? And who are you? It’s “Alice in Wonderland”. Who… are… you? That’s the caterpillar, remember? Why is it so disturbing when the caterpillar asks her that? I remember showing it to my daughter when she was five, six years old. She did not like that caterpillar saying, “Who… are… you?” [laughs loudly again]. ‘But it’s interesting with this film because all the clues are there through the entire picture and I think, without giving away too much, if you see it and you don’t know anything, and you do at least find it satisfying by the end, you might then want to go back and see it a second time or a third time.’

While this isn't him coming right out and saying it, he is hinting that he placed visual clues throughout the movie, logically the bandage being one of those clues, as to what exactly was going on.

I think the wounds wants to show and prove that he really had an argument with George Noyce(the patient at building C),and at the last part of the movie the bandage disappear because it wants to show a couple time passed after all these events.