Continuity mistake: We first see from the inside of the door (and therefore backwards) the instructions that Mr. Miyagi leaves for Daniel to paint the house. In the next shot we see the same note from the outside - from Daniel's viewpoint. Clearly they are two different notes. The left & right arrows switch directions, the drawings of the hands change, the position of Miyagi's signature changes, and the placement of some of the exclamation points changes.
Continuity mistake: In the beach party scene when the boom box is thrown at Daniel he catches it with the speakers facing away from him, but when it was thrown the speakers were facing him.
Continuity mistake: At the beginning when Daniel is playing soccer on the beach, he has a huge sweat stain on the back of his shirt right before he runs past Ali. Moments later, when he runs away from Ali, the sweat stain has drastically reduced in size.
Continuity mistake: When Daniel first moves into the apartment, he kicks the outside door open. Then we immediately see Daniel from the inside, and the positions of the pedals on his bike has changed.
Chosen answer: He didn't lie. That was the company she was supposed to be working for. However, the company went bankrupt and she lost her job. She showed up at the restaurant at the same time that the hostess quit and was hired immediately.