When Kate and Sasha are talking and Kate says "Please, you have to have some idea what this means.". At that time you can see an alien looking person moving reflected in the walls. It moves into view, stops for a second and moves out of view again. This is not Kate because she is standing on the other side of the room. There is also a quiet sound effect as it shows itself. See more...
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Revealing: When Kate opens one of the doors to find Simon on the other side ("Hello gorgeous, miss me? Huh? Come on in, the water's fine."), the shot of her climbing up to open the door is a recycled shot from 42 seconds earlier. It's pretty obvious as the shot still contains a mistake from when the shot was used previously - a boom mic is reflected in the door's shiny surface as Kate climbs up to open it.