At around 1:06, Rheya is lying on a bed with a pillow under her head. In the next shot where she turns to her side, the pillow has magically disappeared.
Gordon says she's getting agoraphobic. Agoraphobia is an irrational fear of going out and facing crowds of people. Gordon is living on a Space Station. She stays in her cabin in fear of meeting the one other person. So it is Agoraphobia.
George Clooney is shown traveling in a sleek slightly futuristic rapid transit train but the rear projection/blue screen out the window clearly shows the current day "Merchandise Mart" station of the Chicago CTA Subway. Also during his journey the train he passes going the opposite direction is a present day subway train.