Shutter speeds for video question
 

I am shooting video at 1080/24 (23.9....)

Mathematically, I guess it's possible to shoot at 1/30th of a second 24 times a second. I've shot a number of clips with that setting and they look "normal" more or less. I've also heard people insist that you really have to shoot with 1/40th or 1/50th shutter speed or you aren't getting 24p, etc.

I'm hoping someone has a sound explanation of whether it matters much for general purposes (okay for certain kinds of motion, panning, etc. I could see a possible reason) and, if so, why, and what kinds of visual differences are going to result.

If you use a shutter speed lower than 1/50th (or 1/48th on cameras which have it) you will get an increase in motion blur. Shooting at 1/30th should give acceptable results but I'd only use it in very dim lighting if you really need it.

This is fine for slow moving subjects like an in interview situation, but will be much more noticible with moving subjects like a skateboarder, or if there is any camera motion such as a pan. It's ok to use in a pinch to get a little extra light, but overuse it and you will start to notice parts of your footage turning into blurry mess.

The general rule is to use a 180-degree shutter, that is, a shutter speed of double the frame rate. A faster shutter speed will give sharper images but motion will be stuttery, while slower speeds result in blurred motion. Both higher and slower shutter speeds can be used to get certain effects but you should be wary and know how to avoid the issues they will cause.

When MUCH slower shutter speeds are used, such as 1/6th, then you are no longer getting 24 individual frames. Shooting at 24p with a shutter of 1/6th, You get 6 exposures, each one repeated 4 times to give a total of 24 very blurry frames.

very slow shutter speeds
 

Thanks for the basic info.

In my brief experience with the T2, it won't let me use any shutter speed slower than 1/30, which makes sense.

Canon used to have a MiniDV camcorder called the Optura (the original one, not the succeeding generations of it) that shot 1/8 sec shutter speed. Basically all this did was record 8 stills of very motion-blurry 30fps video. All it did was create a slow strobing effect. It was great for timelapse though. Each 1/8 sec exposure was repeated for a number of frames. So it is possible to go lower if your gear is set up for it. You just won't get 30 full individual images per second.