Low transmission fluid? Or bad transmission?

I have a 2002 auto Jetta Tdi, 360,000 Kilometers. It has a reverse problem where it will need to be warmed up for 10-20 minuets before it will shift into reverse. On a warm day i can rev the car up to about 2,500rpm and it will "kick" into reverse. Sometimes the car will fight back with me and kick in and out for a few seconds. Once it's warm it will always shift instantly.
Second problem in shifting is when i reverse down hill and put it in drive, or anytime i stop fully; *aka* a stop sign and need to go again (downhill reverse being the worst) it wont shift tell about 2000rpms, unless i keep puffing the gas to 1500rpm and let it shift smoothly. If i wanted to, could get it up to 4000rpm and it would leave a nice black mark, basically just acting like it sticks in neutral before it shifts to first.
Just curious if this is known problem, fixable problem, anything... Thank you for any feedback.
-Josh

Search the forums for your transmission which I believe is an 01m. Plenty to read on many similar problems.

I do not know of any other members complaining about stop and go behavior in reverse. It just isn't something that is usually done...

Like Softrock said, you have a transaxle that is basically long in tooth (large number of miles) and may be past saving. Read threads on the 01M by CoolAirVW and you should get a good idea of what (if anything other than a trans swap) you can do at this point.