Maybe loose brake pad?

Yes, that sounds like a rattling brake pad. Do you have the Carbotech's? I was able to quiet mine with an anti rattle buffer on the bottom of the caliper and more red goo on the back of the pad.

Anti rattle brake pad buffer

Amazon.com: CRC Disc Brake Quiet 05016, 4 Fl Oz: Automotive

Thanks for posting that video. I've been having rattling like that in my car for the past couple of months, but I couldn't figure it out. It does sound pretty similar to yours. The thing that threw me off though is that sometimes I hear rattling when I have come to a complete stop. I installed my Carbotech's about 6 months ago. I guess it took them a while to start rattling.

I know that sound well. My Carbotechs were quiet until I tracked the car, then they made that same exact sound. I just had to re-goo them.

Is this rattle noise only a problem for on the front brake pads?
Are the brake pad buffer mentioned above really needed?

I now have the same noise from the front brake pads (at least it sounds like that).

I particpated when the rear brake pads were installed and we used the "red goo". That was about two years ago, there has been no noise from those. We did not use break pad buffer.

For the front brake pads, I gave the "red goo" to the guy that were installing (and insisted that he would use it and that brake pad noise was a know problem), but he used his own stuff. That was about a year ago, the rattle started being very noticable last week.

The carbotechs rattle because they're not the same size as the OEM pads - there's the brake goo that you put on to keep them from rattling but a good hard braking should settle them (yes 783 has carbotechs).