Other mistake: If the dead characters all are continuously displaying how they died, Adam and Barbara should constantly look wet, but they don't.
Other mistake: When Adam's headless body runs into the hallway to go shut the attic door, you can see a reflection of his body when he crashes into the banister. Ghosts don't have reflections, as seen in the beginning.
Other mistake: If the Maitlands cannot be seen in a reflection being ghosts, then Lydia would not have seen them in the attic window in her camera, as that uses a mirror to reflect the image through the viewfinder.
Other mistake: When Adam and Barbara have their sheets on, trying to scare the mother, they walk out in failure and Lydia takes pictures of the ghosts - polaroid photos fall out (too quickly) and Lydia picks up one which is already developed - they take longer. (00:39:25)
Chosen answer: Because he can't say his own name, therefore the charades is the only way he can get her to figure out what his name is to say it.
Guy