Continuity mistake: When Ryan Gosling first goes to meet Eva Mendez in the diner, she comes from the back and delivers a fair amount of food on three or four plates to the table just behind Ryan's left shoulder. When the camera angle changes to in front of them the table is now visible and has no food or plates on it, with the diners sitting waiting patiently for their food. (00:09:48)
Factual error: When Bradley Cooper is leaving the Police Station in the 1990's, he is being watched by Ray Liotta by the street. You can see a silver 2010 Hyundai Sonata drive right past them, a model that doesn't get built for another decade. There's also a GMC cargo van parked across the street that looks like it was built after 2009. (01:23:20)
Continuity mistake: Luke's motorcycle can't decide if it's a 2-stroke (in the circle cage), or a 4-stroke engine. It seems to be the high pitched wail of a 2-stroker when there's a chase, but has the mellow burble of a thumper when he starts it for his son. This changes back and forth at least 4 times.