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.
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.
When Laura plays "I've been working on the railroad" for Paterson, her right hand is just strumming the air, not touching the strings at any point.
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.