Thank you for the explanation. This is very useful and I appreciate the time taken to write this.+1
Something for the OP to understand here, a lot of the time (not always as there are reference frames), when a camera compresses footage it does so in part by measuring the changes between the current frame and the next frame in terms of pixels. To save space, it simply references the last frame for pixels that haven't changed and encodes those that have changed. When you get movement in a frame, the amount of the picture and thus pixels changing between each frame is much higher, so you now need to pack more pixel information into a given file size, which means using more compression. More compression = more mistakes / approximations = more artefacts.
The 2nd issue is as Kamkar said is the effects of shutter speed. The slower the shutter speed, the further an object has travelled in each exposure and thus the more blurred the detail has become.
See above. Probably down to insufficient bit rate.
Could be any number of factors.
Individual moving objects jumping down the road are almost certainly caused by too high a shutter speed, although what is too high? Remember the penalty for smooth video is more blur. The faster the shutter, the better the stills quality. The slower the shutter the more smooth the video, but the greater the blur on both video and stills and the less chance of recovering detail eg a number plate. If you want detail retrieval, it becomes a fine balance between smooth video and fast shutter. Stutter can be alleviated with higher frame rates. However, if you have to reduce the frame rate when encoding it for playback, then you lose detail again because you either create composite frames ie 2 frames made into 1 with parts from each, or you discard frames. Discarding frames puts you in the same position for stutter as if you had recorded at 30fps to start with. Stutter in the case of moving objects is cause by the object moving a visible distance between each captured frame. That's my understanding of compression anyway, and I hope it makes sense.
Occasional overall stutter, may be down to data writing issues, so maybe the camera can't encode fast enough, which could be a camera hardware issue, a software / firmware issue, or a media ie SD card issue. Might be worth trying a different SD card if you have one simply because not all cameras like all SD cards.