When Sun is looking at the picture of her husband in 1977, Hurley is looking at the camera. Then the scene goes back to how the picture was taken. Right before the camera click is heard, Hurley turns to Kate and Kate turns to Hurley.
During the opening scene, the Ajira airliner is shown flying with the logo on the tail highlighted. This wouldn't be the case as they are flying at night, so the tail would be darkened like the rest of the plane.
Hurley is flying next to his guitar. It is extremely improbable that an airline would let him take such a big piece of luggage on board. It'd have to go to the cargo bay. However, it was stated in 316 (2009) that Hurley had purchased 78 additional seats. Perhaps he used one of those tickets for his guitar.
(16:10) When Juliette gives Ethan back to Amy, it is VERY clearly a doll.
When Sun is given the photo of the recruits of '77, another person is seen in the room over her left shoulder. Only Frank and Christian should be with her.