Is this animation of the angle of attack sensor in this video from 25:30 to 25:50 correct? It seems like motion of the sensor is the opposite of what it should be based on the angle of the aircraft. For example, given an angle of attack sensor mounted on the right-hand side of the aircraft, I would suspect that a strong nose-up attitude would cause the blade on the aoa sensor to turn slightly clockwise with respect to the body of the aircraft. But to me the animation displays a counter clockwise turning for the nose-up attitude.
Maybe, depending on your interpretation.
The animation leaves room for interpretation. It is never specified what remains constant and what changes throughout the animation. For example, is the animation just zooming in on the sensor (and the sensor vane movement is just the entire aircraft pitching), or is the sensor picture relative to the aircraft pitch? Let's assume the latter; in the former case, it's obviously correct but doesn't teach us anything.
The aircraft pitch displayed is the actual aircraft pitch as it is in flight. This means that respectively the situation in climb and in descent is shown. This makes sense with the preceding comments about the vane "being stuck in the climb position". In this interpretation, the animation is correct.
As the plane climbs, the thrust vector has a downwards component. This means the aircraft thrust accounts for part of the gravity, and the wings have to take less of the aircraft's weight. This means the angle of attack is reduced in climb, and indeed the sensor vane will point more 'down' during climb, and more 'up' during descent.
Angle of attack interpretation
The pitch shown in the animation corresponds to an angle of attack (i.e., the air mass is moving strictly horizontally through the animation). In this case the animation is incorrect.
A high angle of attack means that the air has a vertical component w.r.t the aircraft body; specifically, from the belly upwards. The AoA vane is like a weathervane, and will follow this movement. In a high AoA situation, it will point up (in a cobra maneuver, it would point straight up). This is opposite from the animation.
The video makes the angle of attack indicator appear to move backwards because of how we perceive movement. The indicator in the front is moving with respect to the aircraft; at least that is how we perceive it.
In reality, the angle of attack indicator is stationary (with respect to the relative wind) and the fuselage is rotating around the indicator. The perspective is backwards from what we perceived in the video.