When Pete goes to see Jeffery in jail, it says Seattle County Jail. There is actually no such place. Seattle is in King County Washington, and and so the county jail would be King County Jail.
Myka tells the board that she just nailed a one inch light switch from twenty feet away. In reality, she was less than ten feet away and the light switch was much larger than one inch.
When Myka is in Pete's room before she returns his memories, you can see someone's reflection (possibly crew, possibly extra) in the mirror when they walk behind Myka.
At 8:14, they show a panoramic view of Seattle. Immediately afterwards they show a hospital entrance. The hospital is actually Providence St. Vincent Hospital in Beaverton Oregon near Portland.
When the scene changes to Seattle, the scene is identified as "Seattle County Court". There is no such place as Seattle County - Seattle is located in King County, Washington, which is how the courthouse is identified.
In the opening scene where the airline pilot loses his memory and leaves the cockpit, the plane suddenly goes into a nose-down attitude, alarms begin blaring, and the first officer radios in that their landing approach is no longer stabilized. At that point in the landing cycle, the first officer is at the controls and actively taking part in landing the aircraft with the captain. There is no reason for the airplane to suddenly go into an emergency descent simply because the captain left his station, the first officer would simply take control of the aircraft and continue the landing cycle.