You can see the screenshot below. I uploaded it in the highest resolution I could get, but it's from the DVD, so the resolution is set anyway (and SE reduced it anyway). I took out my blu-ray and watched the sequence, frame by frame, on my 57" HDTV (these days it's harder to get a sharper or larger image than that). This screenshot is of the first or second frame of the shot with this object falling. It's the largest and clearest view of the object. This screenshot is from the DVD "Limited Edition." The image on the blu-ray is similar.
Since it's hard to see, here's just the object itself (which doesn't show up well here unfortunately):
While it's not stated definitively, I think it's intended to be his hand, still clutching his lightsaber. If you can find a good image, there is a cylinder stretching out on two ends from something in the center, as if it's a lightsaber held in a hand. But the main part of the object, the part holding the center of the cylinder, there's what looks like fabric fanning out from it and blowing in the wind as it falls. I suspect that's intended to be fabric from his sleeve, but his sleeve is long enough to cover his stump when we see Luke. (I suspect this is an intentional error to avoid showing a severed hand directly and thus allowing the movie to keep the PG rating - there's rumors Lucas made other changes along the way to keep a PG rating.)
When Luke is drawn into the air chute and sliding through it, there aren't signs of anything falling with him. Still, the shape is enough like something clutching a lightsaber that it seems likely it's intended to be his hand.