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.
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.