Revealing mistake: In the sequence initially introducing Hit Girl and Big Daddy near the beginning of the film, where Big Daddy shoots Hit Girl in a training exercise, no bullet hole appears in her overcoat, despite her having to unzip it to remove the projectile from her bullet proof vest. In the wide angle shot, padding from the coat is see bursting into the air upon impact as she is knocked back to the ground. In subsequent shots, no bullet hole is ever visible in her coat either. (00:12:55 - 00:13:48)
Revealing mistake: Throughout the movie, people getting shot almost always don't have the shot angles line up with how they appear. This is especially obvious in the end scene with Hit Girl shooting the gangsters: she might shoot someone at an angle from the side, but the shot appears to have come from directly behind the person.
Answer: It's a modified version of the "Tra La La Song" from the Banana Splits TV series of the 1960s. http://en.wikipedia.org/wiki/The_Tra_La_La_Song_(One_Banana,_Two_Banana).
Jeff Swanson