This is really nitpickin' ;;
When Crono takes a snooze in his own bed, when he wakes up, he will stand on the stairs to his room. Now, no matter which way you move, you'll alway end up in his own room (so when I move right, instead of going down the stairs, I'm back in Crono's room). I'm not sure, if this is because of the Demo, or that it happens in the real game as well.