...Changed it to 720P [...]. What I noticed was that when not zoomed in at all, the video looked ok. But, whenever I zoomed just a little, the picture got very grainy right away. [...] All this was done indoors, but with lots of lights on, except when I tried the dark to ligh thing, of course
Just looking at the specs for your camera, three things to note: ONE, you have fixed focus; TWO, you have a aperture fixed at f2.8; and THREE, you have a digital, as opposed to an optical zoom.
To start with, the point of optimal focus is pre-set in your camera. It doesn't specify where that point is, but it's in some convenient middle range where the majority of video is taken, say six or eight feet away, for example. Things in more in front or more behind that point are increasingly less in focus, according to the "depth of field"--the range of what is crisply in focus in the image. With a aperture of f2.8 you have a fairly narrow depth of field when shooting. Search the terms "depth of field" for more info on why.
Now, because your aperture is fixed, exposure (how bright and dark the image is) is controlled through either shutter speed or gain, or both almost certainly for this camera. Let's focus on shutter for now. In low light (which I would classify the performance sample video on YouTube) likely your shutter speed might slow down to 1/30th of a second, perhaps less. With a slower shutter speed any movement in your hand or subject can cause blur.
Next, all of the above is exacerbated with a digital zoom. Digital zoom merely crops or "magnifies" the image that is being processed so that to you, it seems like you zoomed in, as with an optical zoom (think of a camera where the lens lengthens or shortens when you zoom). But it isn't. The image is essentially "scaled up" to appear zoomed in. But now that it's "magnified" you can notice the imperfections more easily. The result is that it makes things that are out of focus look more noticeably out of focus. This is in part why shooting at 720p makes the problem less evident. There is less resolution to notice what is and what is not in focus. Dropping down to 540p would probably make the blur seem even less objectionable. Try the three different resolutions out in similar low light circumstances to see for yourself.
So this explains why in your performance footage--low light, slow shutter speed, using digital zoom--you have a blurry image, while in your bright Turks footage (bright light, fast shutter speed, as far as I can tell, no digital zoom) you have a much crisper picture.
One last thing, regarding the grain. As I noted above, when in low light situations, since the camera cant allow more light in via the aperture (remember its fixed at f2.8) and let's assume the shutter speed is as low as it can go, the camera has only one more option to "brighten" the image: It electronically boosts the sensitivity of the sensor, which is called "gain". But while the camera is now more sensitive to light, it also produces more grain. As with the blur noted above, the digital zoom makes grain more evident by in effect making them bigger as it makes the entire picture bigger. The bigger the grain, the more noticeable it is.
I also noticed it takes a loooooong time for the camera to correct if you pan from low to more light. Everything in the lit area stays very red/orange for about 30 seconds. All this was done indoors, but with lots of lights on, except when I tried the dark to ligh thing.
This camera probably has a built in circuit to slowly adjust the auto white balance as color temperature changes. Presumably, it's to prevent very fast white balance changes to make them seem less objectionable.
Hope that helps.
