The second time Booth sneaks to first class, Bones earphones are off when the camera is aimed at her, but when it's aimed at Booth, her earphones are still on. It goes back to her and they're down again.
The first time Booth sneaks into first class, he catches the 16 year old boy stealing alcohol from an unattended beverage cart that is right next to him. The flight crew would never leave a beverage cart unattended like that for exactly that reason. They would be responsible for anyone underage who stole alcohol from the cart.
The 16 year old boy when finally accused and waiting for the return flight, has one end of the handcuffs on him but the other end appears to be just dangling. However, the other end is fastened to a seat belt.
A Great Circle route to Shanghai from Washington does not fly over Greenland. It misses by about 500 miles to the West.