One could think of the ransom note as a means for the killer to misdirect the police investigation. If you remember that (oft-spoofed) film, the Usual Suspects, a story is fabricated from elements taken from bits and pieces (the mug, snippets on the wall, etc). Now, JonBenet's killer, thinking along similar lines, could have taken elements from the house and incorporated that into the fake ransom note to subtly implicate the Ramseys: SBTC from the plaque in John's office, movie references thinking that the Ramseys are movie fans (from the posters), the similar handwriting (several attempts were made to try and match it with Paty's).
The ransom note was amateurish because it was not intended as a ransom note, it was intended as a way to mislead the police and to cast suspicion on the Ramseys. Of course, when John was questioned whether he believed the note was used to frame him, he had to dismiss it as a stretch because to say, 'someone tried to frame me' would look even worse!
Anyway, I may or may not believe the above. I'm just floating it as an idea to explain the movie references. After all, "The greatest trick the devil ever pulled was convincing the world he did not exist. And like that... [JonBenet's killer] is gone."