UPDATE: As I continue to tinker with render settings, I'm noticing that the bright speckles also show up on some non-glossy/non-SSS materials. It seems to have something to do with distance from the camera and perhaps the size of area and/or point lights. As far as I can tell, converting an area light to a point light creates more speckles, whereas shrinking an area light makes more speckles in the background and fewer in the foreground.