After the Observer disappears, a bundle of monitor wires can clearly be seen tucked into Peter's shirt, yet he walks away from his original position a minute later without ever touching them. He turns back to the camera and they are gone.
Olivia only cuts Peter's left hand and foot free, she never touches his right side, which is on the floor. He gets up and there is clearly a zip tie strap laying where his right wrist had been.
During the test where Olivia tries and fails to turn on the lights in the box given to her by Jones, the box is shown with all lights illuminated in the cutaway, but they are all off when the camera returns to the box.
The battery clamp over Nina's right hand is put on twice. The first time the window shade is raised and again a minute later in background.
When David Robert Jones brings out the wooden box with the LEDs, Olivia recognizes it and immediately assumes that her test is to turn the lights on mentally. In the original test, the task was not to turn the lights on but turn them off after they have all been activated by the switch, still visible on the prop. It makes no sense that Olivia should jump to the conclusion that goal of the test is to turn the lights on since the box has never shown that function before.