Rather than try and polish, clean, and generally hope and pray that I could re-use my current 6-year-old headlamp assemblies in my 2003 Jetta, I decided to just straight-up replace them. I also checked the Exterior Lighting section of the How-To thread and found that the current link to "Golf/GTI Headlight removal (Jetta too)" is dead - so here you are:Mods: feel free to use this post or to point people to my personal website. Thanks, yo.
Time to complete: ~1.5 hours
Tools used:
6 Piece Offset Star Drive Wrench Set available for $8.00
Philips screwdriver
Flat-head screwdriver
To start, pop the hood and remove the center grille with the VW logo on it by pressing the center tab in with a flathead screwdriver (red arrow). The grille will move forward and ultimately upwards:
Pull up and outwards on the tabs on the sides of the center, VW grille to release it from the body mounts:
With the grille moving forward, you can see that the hood release will have to be un-clipped in order to be able to remove the whole assembly.
To unclip the hood release, flip up the metal retainer that keeps the plastic fork of the clip from spreading:
I used a flat screwdriver to spread apart the fork of the hood release – once spread far enough apart you’ll be able to get it off the pin holding it to the internal hood release and the center grille will come off the car entirely. Once the grille is off, you’ll want to remove the five Torx screws holding the bumper cover on:
Next, remove the small screws holding the bumper cover on from inside the front wheel-wells. This allows you to be able to pull the cover forward enough to expose the headlight mounting bolts without pulling at anything too hard and breaking oft-fragile clips:

At this point you should be able to pull forward on the bumper and down a little, exposing the underside of the headlight assembly and the two hex screws holding the assembly on (red arrows). A really long, skinny hex driver is perfect here – even more perfect if it’s magnetized as the screws tend to fall out into the interior of your bumper easily:
On the driver’s side, remove the two Torx screws holding the headlight and remove the two Phillips screws holding the cover that’s on the backside of the headlight assembly – this will allow you to get to the headlight plug. No need to remove any cover on the passenger’s side.

Insert a flat screwdriver into the headlight plug assembly and gently press down to unclip the plug from the socket on the back of the headlight assembly:
At this point you’ll be able to remove the entire headlight assembly through the front of the grille. Reassembly is literally the opposite, with replacing the assembly, mounting it with the Torx screws, reconnecting the wiring harness and remounting the bumper and grille. One hint: I mounted the headlights and tested them by plugging in the harness, running through low beams, high beams, turn and hazard signals before really replacing all the various screws and covers. The last thing to remember is to aim your headlights properly, which is covered in general by the Mid-State DeLorean Club (you can’t make this stuff up…) as well as by any Google search on “aiming headlights.”

Modified by sweater at 3:51 PM 7-26-2009
Modified by sweater at 6:20 AM 7-27-2009