In Tim's upstairs garage apartment there's a cone fireplace. Sometimes it's freestanding in the middle of the living room and in other episodes it's in the corner with a brick surround.
The first seven episodes of the first season showed a copyright date of MCMXLIII (1943) instead of MCMLXIII (1963). This was corrected in episode eight.
Throughout most of the first season, the wires supporting various "levitated" objects are obviously visible.