Sloan tells Don that Erin Andrews was mobbed by paparazzi after seeing Man of Steel at El Capitan in Los Angeles. Since 1989, Disney has owned El Capitan and only shows their films there. Man of Steel was released by Warner Brothers (and produced by DC Comics that rivals Disney-owned Marvel) and would not have been playing at El Capitan.
At the Moscow airport when Maggie and Jim wait in line for the tickets, the PA in the background says in Russian: "Attention, attention! Boarding continues for the flight to... Southern Urals". Southern Urals is about five times the size of Alaska and includes the entire country of Kazakhstan. Usually airlines are a bit more specific about where their flights go.
When Jim Harper and Maggie Jordan kiss, ostensibly aboard an airliner in flight, a green light sweeps across their faces several times. The background sound is consistent with a jet plane in level flight, with engine and slipstream noise. The green light, which seems to be coming from a rotating lamp on a road going vehicle, possibly a nearby fire truck, suggests that the plane is parked on the ground. The only green lights used on aircraft are anti-collision lights that shine away from the aircraft, and do not rotate or flash.