At the end, when Kate is standing on the edge of the exit of the Hypercube, you can see her through the exit in the shots from below. In the shots from the top however, the black door of the exit is still closed.
When Mrs. Paley discovers the dead scientist in the other room, she sees him lying on the floor. But when Jerry enters the room he says that there is a gravity-shift (which would have made the dead scientist look like he was lying up against the wall). They disorient the viewer by shooting the 'dead scientist'-scene sideways, but gravity is still in the same direction as in the previous room.
Jerry's watch has a different serial number than the watch they find in one of the rooms. This might not be a true continuity error, because in a parallel universe his wife might have got him another watch from the same brand and series.
When Jerry climbs into the room where Dr. Rosenzweig is he says the gravity shifts, but after the picture has rotated 90 degrees clockwise he climbs down the left wall, which is the same direction he came from, only seem from another angle. If the gravity had shifted he would have had to climb in any of the other directions.