I would argue that the two main themes in this engaging short story are the supernatural and paranoia.
Since multiple members of the family all heard the mysterious footsteps downstairs and coming up the staircase, the reader is led to believe that there really was something down there. The idea of the supernatural is central to the story, because It’s not as if the noises were only heard by one person and could have been imagined. When the police arrive, they point out that the house is well secured, with all windows and doors “locked on the inside tight as a tick.” By process of elimination, since it was not a member of the family walking around, and there could not have been a physical intruder, then the pacing sounds that had been heard must have been made by a ghost.
Any story about the supernatural is likely to include an element of paranoia, but in this case, it is the neighbors, the police, and the grandfather who slept through the initial commotion who display paranoia. The theme of paranoia can be seen in Mrs. Bodwell’s instinctive reaction that due to the “intruders” next door, she and her husband need to sell their property and move. Further paranoia is displayed by the police, who question the narrator on his arrival, even though the fact that he is clad only in a towel would seem to indicate that he is not an intruder. When the police ascend the stairs to the attic, the grandfather shoots first and asks questions later, due to his paranoid belief that “the police were deserters from Meade’s army.”