My wipers had started to run slow.......... dying sort of on my 2001 A4 Quattro 1.8T.  Anyways, decided to have a go at them and pretty much fixed it for now.  I have a feeling the assembly arms attached to the motor will eventually have to be replaced somewhere down the road though due to the pitting in the wiper spine that inside the wiper pivot housing.  More about that later. 

Anyways, I'm not a mechanic, so the usual blah, blah, blah about doing this at your own risk and I take no responsibility if you follow this advise and pooch your Audi.  And sorry in advance for the non-technically correct use of vocabulary!!

This took me about 2 hours to complete, going slowly, no manuals, no help, no previous experience.  Mind you, I do know a little bit about how to get around cars to disassemble and re-assemble them. Things you'll need are the following (if I remember right!!):

8mm socket (plastic panels)
10mm socket (wiper motor assembly)
13mm socket (wiper arms)
small flathead (to remove small c-pin)
small hammer ( to knock out spine from housing)
cleaning product (degreaser, lubricant, rust removal gunk)
High temp grease (or whatever you like)
Lots of rags
Piece of cardboard
Container (to put screws/bolts/parts in so you don't loose them)

If this is happening to you, this is what you can do to fix this problem BEFORE you kill your wiper motor.  Open the hood, removed the panel that covers the battery (rubber trim in front of it and then pull towards the front), then remove the wiper arms (with the hood up), next remove the 2 plastic panels covering over the wiper assembly just under the front window.  I also covered over the exposed battery terminals so that I wouldn't accidentally drop something onto the battery and short it out (hello Mr. Murphy!!).  Now run the wipers for a few minutes. Then where the wiper arms attach/bolt to the wiper assembly, drop your finger down on that shaft and see if it's hot for both the passenger side and drivers side.  If it's hot at all, the units are seizing up.  My driver's side was smoking hot. You then have to remove the wiper assembly and wiper motor.  Three bolts hold that all in--10 mm bolts with green-ish heads.  Also don't forget to unplug the motor.  It takes some jimmy-ing to get this assembly out.  I also removed the black plastic cover off the box in front of the wiper assembly.  The trick is to move the wiper assembly arms around to work the whole unit out.  Be patient so you don't kill anything else and make this project a BIGGER one.

With the wiper assembly out, where the wiper arms attach to the assembly, clean that off well.  Next remove the motor front the assembly (3 bolts and then the main nut).  Back on the where the wiper arms attach to the assembly, you'll notice that there is a very small C-ring that snaps into place on the top of this area just below the spines.  Carefully remove it.  Then take off the washer and gently hammer down the core and remove from the bottom (there's two washers at the bottom.... Don't loose these).  A rubber grommet should also appear at the top.  Don't loose this either!! The core and the outer assembly must be cleaned thoroughly and all grime, calcium, rust, etc removed.  That junk is causing the thing to heat up.  I used a combination of screw drivers, a small file and various other things I could find to clean this up.  On note though, try not to scratch up the smooth areas on the housing or the spine.  Just try to attack the pitting and corrosion areas.  I re-assembled mine and packed it with high temp grease.
In the re-assembly, two washers at the bottom, housing, then at the top, rubber grommet, washer and finally the c-ring.

I re-assembled both sides after cleaning them both and also reattached the motor.  Next I put down a piece of card-board and re-plugged in the wiper assembly.  I then ran it while spraying a liberal amount of liquid lubricant to free up the ball joints and get the rust and grime out of them.  Make sure that when you do this, the assembly is safely on top of the cardboard.

Then I re-installed the assembly.  One thing here that I learnt the hard way,  re-assemble everything but DO NOT PUT ON THE wiper arms. First, gently clamp on a pair of vise grips to the passenger side and turn on the wipers to ensure that the wiper arm does not go down into the engine compartment when it's turned on !!!  Initial placement of the motor to the arm assembly is critical.  The center nut on the motor must attach to the arm with the arm pointing directly across to the passenger side in parallel with the lower edge of the window.  I ended up having to undo that center nut (while the whole assembly was installed but don't take it right off, just loosen so that the arm is loose) and adjust that first arm to the correct location.  I then tightened down the nut as much as possible, jumped back in the car, turned on the wipers and shut the car off to stall the wipers in the up position in order to fully tighten down this nut to the wiper motor.

I then tested and the thing runs mint again.  One note, because of the corrosion inside the pivot housing (where the wiper arms attach) it's possible that this is only a stop-gap measure.  If you are concerned about this, when you take out the wiper assembly, remove the motor and just replace the arms completely.  Costs more, but then also possible you won't have to take out the either thing like I may have to, but I'm chancing it !!!

If you have any questions, feel free to email me.  I may or may not have answers !!!