When Betty Hutton (Annie) sits down on the bench to start singing, "Oh, you can't get a man with a gun," she opens her mouth to begin singing. In the next scene you see her open her mouth again and start singing!
I taped this movie off of TCM and saw the same blooper. A minute later (during the same song), Betty Hutton is sitting on the back of the bench with her gun in her lap pointing to her right. a frame later the gun is pointing to her left!