No, you don't need the wheels on jack stands, when you 'go through the gears' (what we call it at work) you are just going from the lowest gear on the selector (ie "Low") all the way to park, 5 secords in between. Make sure you have your foot on the brake at all times, e-brake on for extra safety. The gear selector pattern should be something like Low - 3rd - Drive - Neutral - Reverse - Park.

When I do this at work, I am working from a basement, with the car on ground level (I work for a Jiffy Lube type company, except we are actually good and reliable. We are ranked in the top 50 among quick lube shops nationwide)

 

I have a 1997 A6 Quattro that had some of the same issues mentioned above. I was worried that I needed an entirely new tranny. Luckily, it turned out that the transmission lines were only leaking. I had the lines replaced by my local mechanic along with new Audi tranny fluid. The whole job cost me less than $300.00. When I drove the car for the first time, I could not believe the difference. The car now shifts so smoothly that the shifts are hardly noticeble.

 

My 1999 A6 tiptronic does the same thing. It really doesn't like to shift out of second when the engine is cold. I'll often upshift myself.

 

When the car is cold the transmission will "hold" to speed up the warm up of the car. I think this should be mentioned in the owners manual.