There's fuel for the chainsaw, and once it's functional, you can cut down the wooden fence at the pool!
You can find the fuel in Zak McKraken and the Alien Mindbenders.
You can go up the Out-of-Order stairs on the first floor to access the top floor without going through the whole house.
In the NES version, the key pad on the inside of the security door (where the nude statue would be in the PC version) had a working code that would open up a secret passage or elevator that gave full access to all rooms in the house. Supposedly, this passage/elevator was how family members got through the house quickly without running into the player.
While all the keypad did was blow up the mansion, there were points in the game where the player should normally have seen a family member, namely Dr. Fred, before or after a cutscene, but never did (i.e. Dr. Fred goes into Ed's and Nurse Edna's room on a few different occasions, but even if team member is parked in the main halls, they would never run into him). However, on some occasions, such as Weird Ed getting food for his hamster and Nurse Edna capturing another team member and returning to her room would find and subsequently imprison a team member if they are parked in a main hall way before or after they move out.
Playing a recording of the Tenticle Mating Call in the room with the Green Tenticle as a female character (Wendy or Razor) would cause him to rape the character.
Playing the recording of the Tenticle Mating Call in the Green Tenticle's room would cause him to kill you, male or female.
In the PC version, there is a famous area where you can put a hamster in a microwave and kill it. When the game got heavily censored and released on the NES, this part was not removed on US copies due to an oversight by Nintendo. It has been removed in the PAL version and later releases of the US version. (evidence)
As a part of the game, if you give Weird Ed the hamster bits, he will kill you, and this feature still existed in the NES version of the game. However, in the NES version, after the team member was killed they would still be able to move around as a spriteless "ghost", though, their entire inventory would have been cleared. They could still gain new items and interact as if they were still alive.