I think the "I'VE DONE IT" tattoo is an important plot point and maybe even the climax of the movie. Its appearance is a sign Lenny realizes -- if only for a moment, before his next memory lapse -- that he has found a way to get some vengeance and also end his run of murders.
Lenny has just written himself a note to get a tattoo of Teddy's license plate number. He does this to punish Teddy because Teddy has just confessed to using Lenny. Lenny knows he himself will soon forget the confession and everything else that just happened. So Lenny decides to sentence Teddy to death, by getting a tattoo of Teddy's license plate, which later will make forgetful-Lenny think Teddy is John G.
The image of the "I'VE DONE IT" tattoo depicts Lenny just after writing the note to himself about Teddy's license plate -- briefly savoring a moment of victory in the form of a quick day-dream where he is with his wife, laying in bed, a proclamation of victory freshly inked on his chest.
Immediately after the appearance of the image with the "I'VE DONE IT" tattoo, Lenny's memory resets. Lenny is sitting there, having forgotten everything that just happened in the previous 5 minutes or so -- but holding that fateful note about Teddy's license plate, which will indeed lead Lenny to eventually kill Teddy, giving him vengeance and
presumably ending his string of murders.
See for yourself: watch the scene again.
23 Dec 2014 EDIT: As mentioned in Bajur's answer, there is a mid-movie scene where Natalie is touching a blank spot on Lenny's chest, right where the "I'VE DONE IT" tattoo would be, and asks "And what about here?" Lenny answers : "Maybe it's for when I find him." I think that dialogue shows Lenny was saving the spot on his chest for when he catches the man he is looking for -- confirming that the moment where he "sees" himself with the "I'VE DONE IT" tattoo in that spot is a moment when he knows he has accomplished his goal.
7 May 2017 update: confirmed by critic Andy Klein in an analysis for Salon.com:
The scene of him and his wife in bed, the triumphant tattoo on his
breast, can’t be a flashback. We’ve seen already that he doesn’t have
the tattoo, so he can’t have had it in the past. How can he remember
lying in bed with his living wife, with the tattoo “John G. raped and
killed my wife” visible on his chest? It has to be a fantasy, which
would make sense in the context. He thinks he has just avenged her (or
has just set in motion a plan to avenge her). He’s visualizing his own
sense of satisfaction and peace.