Passat (B5) :: Won't Gear Out Properly - Downshift While Stopping - Sputter While Accelerating?

This is what is happening:

1. When you start driving the car it accelerates fine until it gets to second gear where it keeps accelerating, then you feel a jolt, the odometer jumps 1-2 notches, and it switches into third.

2. When stopping it downshifts fine until second gear getting ready to switch into first to come to a complete stop and again it "jolts"

3. (Sometimes happens) When driving ~25 mph or ~40 mph while continuously accelerating you let-off the gas and then reapply, it stops accelerating and kind of "sputters" and can not accelerate anymore, I have to stop put it in Park and then again put it in Drive and only after that it works fine.

I have taken it to the VW Service and the mechanic could not replicate what I said was happening so I drove with him in the car and replicated the first two steps 3 out of 6 times. He told me that they checked the codes and could not find anything malfunctioning. I told him that clearly something was wrong with the transmission and I wanted something to be done. He agreed that he also felt what I was talking about but it was not enough to come to a conclusion to what was wrong. I mentioned that I wanted this to be written down in the service report, because if something happens they will be aware.

The problem now is that the "jolting" and the stalling-out has gotten worse since the visit to the service 1 month ago. What might be happening and what I need them to repair/change on my car. I am planning on making a visit sometime this week. The first two steps happen when the car is cold or when I switch over form Tip-Tronic to automatic. But that is not always the case.