Maddie and Wally drive around the school in a golf cart and no one notices. They also drive through stacked water coolers while the other ghosts destroy random objects and even set the field on fire. No one alive can see them or the objects as it has previously been established that ghosts can grab an object that will become a ghost duplicate in their hands, unseen by the living world.
In the "field day" meeting, Wally Clark mentioned American Gladiators. Wally died in 1983, while American Gladiators came out in 1989, so he should have no clue about the show; but, even though Wally died before the creation of the Gladiators show, he was school-bound while living students would have been talking about it. He would have also seen magazines with them in it, folders they appeared on, posters hanging in lockers, etc.
In a previous episode, the ghost counselor stated that they cannot manifest energy to move objects or touch people. Maddie kicks a locker and it makes a thump, but it's only a thump other ghosts (and viewing audiences) can hear.
It is revealed early on that ghosts can move objects in a way that is only perceptible to other ghosts. The destruction on field day is a prime example. Maddie moves the panel in the wall to reveal the money and Simon is able to see the money behind the panel.
When Maddie looks through the 1962/63 year book, a teacher is referred to as Ms Bailey. At that time, she would have been either Miss or Mrs Bailey. The title of "Ms" was not in common usage until 1972, ten years later.