Revealing mistake: In the beginning of the movie, when Michael removes the knife from the drawer, you can see the blade bend.
Revealing mistake: When Michael is young, at Christmas, Dr. Loomis approaches Smiths Grove. There is snow on the ground, but the leaves on trees are green.
Revealing mistake: In the rape scene, the guard hits Michael in the back with a baton. It leaves an indent in the material of the suit he's wearing underneath his robe.
Answer: He was hoping that Laurie would realise that she's really his sister. However, because Laurie was just a baby and raised by another family, she had no idea why Michael was showing her the picture or what it had to do with her.