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I think it's likely that Stan copied the complete Journal 3, based on the concern that Dipper would fail to live up to his promise to use the information only for defense and it would be neccessary for Stan to come to the rescue at some point. Stan isn't a natural born scientist, or very studious, but he knows the importance of being prepared to a nefarious scheme, and his concern for the saftey and security overrides all other concerns.
Stan refuses to loose another family member on his watch.
Stan is also not the trusting sort to rely on promises. Recall his precaution in using a tape recorder to enforce Dipper's promise to stay at the Shack Party ticket stand all night.
But Stan is also not the type to hold people to their responsiblites 100%. Hence Dipper had plenty of time away from the ticket booth to clone himself. Seeing Dipper stay long enough to take enough people's money to fill the room seemed to be good enough.
Stan was willing to play along, chasing a dollar bill on a fishing line, rather than spending time checking up on the status of the Ticket Stand. Which incidentally made him more in profit with every sucker than a single bill could be worth. Stan could not have avoiding seeing a Dipper up in the rafters when he rolled his eyes, but since paying customers were obviously still coming in the door, Stan let it go.
Stan tolerates and even encourages the kids to outwit him, obviously justifying it as better preparing them for the real world just as Stan's father did for him.
Witness Stan's tolerance (up to a point) of Wendy's slacker attitude at work. Besides, Soos is more than willing to take up the slack.
There is another consideration to Stan's photocopied version of Journal 3. None of the sections written in secret UV ink would be present. There is also the demonstrated vulnerability of the copies to water.
I find it interesting that miniature versions of the Journal's drawings did not come to life when Stan copied them. Not even the ghosts. Maybe Stan used a different copier setting? There were three other buttons that Dipper never used. What do they do?
Nor were there disembodied Stan Hands created with every single page spread he copied.
Maybe someone should ask the Handwitch?
Bad Thought: Pity the Merperson clone created by the copier! Talk about zero life expectancy!
When Bill turned Ford into a backscratcher and took the three journals from Dipper, we saw the three books levitating in the air surrounded by mystically summoned flames.
Mystic flames, as opposed to good old normal earth-type oxidation with its boring old well tested and documented properties.
The three books float suppended, flaming but not noticably altered, for several seconds.
One Journal is seen falling to earth--still aflame, yet still in one piece. The last evidence we see is a single page spread, scortched around the edges. Yet the page is still largely intact.
It certainly doesn't resemble a page from a book burned by normal fire. Real fire doesn't carefully pull pages from their bindings and destroy them one-by-one.
And even if Billfire DOES work that way, the fire is actually extinguished as the page is blown away by the wind. It's reasonable to assume that the scortched and loose pages are blowing around the deserted city like so much litter.