Possibly a character point, but Paterson tells the Japanese poet that William Carlos Williams was from the city. Williams was actually born and lived in nearby Rutherford, although he is firmly associated with the city through his well-known long poem Paterson, a copy of which is prominent on Paterson's book shelf.in a number of shots.
After Paterson has come home on the first Monday, there is a shot of Laura adjusting the curtains she had just decorated. She then walks into the kitchen. There's a shot of Paterson sitting down on the couch, and the very next shot is her back at the curtains, this time admiring them. Some would think that she would've had to be very fast to get all the way back to the curtains in time, however between the shot of Paterson sitting down on the couch, and the very next shot of Laura back at the curtains, admiring them there is an Ellipsis. Repetitions and ellipses are two of the most identity trademarks of Jarmusch's style.
It's made clear that Paterson doesn't own or use a cellphone, but when he has to borrow one, he dials it using his thumbs. A person not used to texting on a cel phone would use his index finger to dial.
In "Glow", Paterson writes about 'going downstairs to put the coffee on' but he lives in a one story house. That could be seen as an error, however even if he lives in a one story house, it has a basement. "Going downstairs" means going to the basement where Paterson has the small room where we see him writing and reading.