Stanley's room is the subject of the episode Carpet Diem. We can deduce a few things from it.
calendar
July 4, 1982
This is believed to be the date of an important event in Stanley's life. See this page for more details.
owl
According to Stan's Tattoo (DGttU), all secret societies worship a barn owl. Owls pop up all over Gravity Falls. I'm not quite sure what this means, but owls will definitely play a factor later in the series.
rainbow pyramid
Continuing the trend of referencing Bill Cipher and Illuminati symbols.
Experiment 78
clockwise and counterclockwise arrows
body swapping properties
OK. We know Stanley was likely an inventor. According to my theory, he was the mastermind of his secret gang, which included McGucket and later Stanford.
rimmed glasses
The rimmed glasses are the same as the ones seen on Bill Cipher's wheel. Now, they could represent Stanford, but he already has the first symbol on his fez. I think they represent Stanley.
Stanford's mood shift
Stanford seemed to be grumpier than usual on this day. It could easily be because the room reminded him of the date when his brother was kidnapped.
