The passwords work like this:
On the main menu, there is a gold key.
Click on the gold key.
A box appears under the key and you can type in the password.
Click on the gold key and you are taken to the password's room.
The first password takes you to Room 4 and gives you 200 points.
There are, as far as I know, two other passwords.
Because this is a MacroMedia Director game, it is possible to type in a password, go immediately to the last room, open a safe which contains the vital key and then leave the Mansion without having solved a single art-based puzzle.
Not that there would be much point in doing that....