Edited for clarity. 2.Sept.2010
I did play around with the Kinect while at GamesCom, but it was limited to one short session. Yesterday there was a press event at the Microsoft Xbox Offices in Prague with the Kinect being the main piece and so for a couple hours I got to watch and play and form some opinions on the whole thing.
First off, the units in Cologne at GamesCom weren’t production units. In fact they weren’t all that fantastic, to be perfectly honest, as we had some problems getting them to recognize us properly and play wasn’t all that smooth. Those issues were mostly gone with these newer units I saw in Prague yesterday. It seems that they still have some minor sticky points but were far better and faster at recognizing people and movements. That was promising as I was worried this was going to turn into another camera-based gaming fiasco (remember those old PS3 Eye games that couldn’t discern between you and someone else?).
We are pretty much in the home stretch as there’s only about two months left. It’s set for full launch this November 10th.
Some time back some tech specs were put out for the units and looked like this:
Sensor
Colour and depth-sensing lenses
Voice microphone array
Tilt motor for sensor adjustment
Fully compatible with existing Xbox 360 consoles
Field of View
Horizontal field of view: 57 degrees
Vertical field of view: 43 degrees
Physical tilt range: ± 27 degrees
Depth sensor range: 1.2m - 3.5m
Data Streams
320x240 16-bit depth @ 30 frames/sec
640x480 32-bit colour@ 30 frames/sec
16-bit audio @ 16 kHz
Skeletal Tracking System
Tracks up to 6 people, including 2 active players
Tracks 20 joints per active player
Ability to map active players to LIVE Avatars
Audio System
LIVE party chat and in-game voice chat (requires Xbox LIVE Gold Membership)
Echo cancellation system enhances voice input
Speech recognition in multiple (meaning more than one voice)

It is possible that some of these have changed since then (that was July) but it looks about right from what I was told in Prague.
The sensors are capable of tracking 6 different people and 20 points in the human skeleton including hands, wrists, elbows, shoulders, neck, head, hips, knees, ankles and feet. That might be 2 points for the hips and maybe one in the spine for sensing leaning to and fro.