The ND filter is likely allowing your shutter speed to slow down a bit by allowing less light into the lens. Here's the full explanation with a great video:
To prevent stutter, the shutter speed should be more than half of the frame rate. In other words the denominator of the shutter speed should never exceed more than two times the number of frames per second.
For example, if the frame rate is 30fps, you should never have a shutter speed faster than 1/60 (so 1/50 would be ok, 1/100 would cause the stuttering effect).
So, in the above examples, I would expect some stuttering for all except the 60 fps example since they're shot at 1/00.
Again, the explanation is well done in this video starting at about 21:00. But basically, if the camera is recording a very short slice in time (1/100's of a second) just 24 times each second, moving objects appear to jitter or stutter from their position. If the shutter speed is longer, each frame will blur just a bit but this will smooth out the transition from one frame to the next.
This is where ND filters come into play. On a bright day, you simply can't shoot video at 1/50 speed because everything will be overexposed. If you darken the lens with an ND filter (or 2), the camera can shoot properly exposed video at a much slower shutter speed thus smoothing out the video.
Hope that helps!
Chris
