Are gaps appearing when you try to put the cover on and you can not get it tucked under? 
1 -Try cycling the soft top a few times to "loosen" up the joints & lower the top further into the bootwell.   If that doesn't work, see your dealer.

For more tips on installing your 2002 or 2003, 2004, 2005 boot cover - with pictures - check out this page.
 

Part #s: 
2002: 2W6J-19G17-AA
2003:3W6J-19G217-CB - quick reference guide
........3W6J-19G421-AB - hardtop interactive guide
2004: 4W6J-19G217-CA
2005: 5W6J-19G217-AA

to download those guides from the internet, visit motorcraftservice.com >  owners info
 For more hardtop information visit my Hardtop page

• Retract the convertible top to the open position.

• Wipe the surface with alcohol, using the lint-free cloth that came with your vehicle.

• Select the piece that was cut for the driver-side front (DSF) area of your vehicle and remove the backing paper.

• Starting at the rear of the door opening, apply the tape to the quarter panel. At the rear corner curve, fold the flap downward so it wraps around the edge of the sheet metal. Slowly use pressure while applying the tape, pressing to smooth out wrinkles and air bubbles.

• Repeat the above steps for the passenger front trim piece, the driver-side rear (DSR) and passenger-side rear (PSR) pieces.

If a customer wishes to have supplemental parking lamps installed on a 2002-2005 Thunderbird, order wire harness part number:
# 1W6Z-15A434-AA for the 2002-2003 Thunderbird
OR
# 4W6Z-15A434-AA for the 2004 to 2005 Thunderbird

plus 2 lamp assemblies (1W6Z-13200-AA).

To install, First remove the front fascia and remove the existing wire harness at C133. Install the new wire harness, remove the lamp opening insterts from the front fascia,and install the new lamp assemblies. Reinstall the front fascia. Verify tha Fuse 1.03 is installed in the underhood fuse panel. Refer to workshop manual (Section 501-00) ad wiring diagram manual (Section 92) for additional information. NOTE:Installation of the supplemental parking lamps violates Canadian vehicle lighting laws
Dated: 5/14/2004
 

(2005) - 5W6Z*16178*BB ORN ASY FRT FNDR LH  (anniversary blade or sabre)
            5W6Z*16178*AB ORN ASY FRT FNDR RH  (anniversary blade or sabre)
You'll need the right and the left hand sides - they are different.
To Remove:  There are 3 tabs on the "ornament."  Those tabs will need to be pushed back thru the holes in the fender to release the ornament from the fender.
Open the hood and you'll have access to 2 of the tabs.  Open the door and you'll have access to the 3rd tab.  Using a long screw driver, push them thru the holes.  Takes about 10 minutes to get this done for both sides.  Only seconds to replace the ornaments as they snap into place.

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Proper operation of the short drop glass requires that the windows be
calibrated. Though your windows will have been calibrated before
your vehicle is delivered to you, it is possible for the windows to
lose calibration.

If a window loses its calibration, your short drop
feature will lower the window, but will not raise it again when the door is
closed. To re-calibrate the window, press the up switch to raise the
window until it completes its travel and hold the switch down for 2
seconds. 

Another possible effect of lost calibration is that the feature
may not lower the window. To re-calibrate the window in this case, lower
the window until it completes its travel and hold the switch down for 2
seconds. Immediately after releasing the window down switch, press the
up switch to raise the window until it completes its travel and hold the
switch down for 2 seconds.

1 - Make sure window drop feature is working.
2 - The following are excerpts from a forum that should help you:

Removing the plastic header. At the front (towards the front of the car) of the hardtop on the interior side is a plastic panel that runs the width of the top. It is the only piece of plastic there. If the top is on the car, move the sunvisors fully down, lower the windows, and slip your finger or flat firm object between the headliner and plastic piece on the driver’s or passenger side of the car. With a little pressure the piece will stat popping out of position. Fully remove the piece. You will see the adjustments screws on the left and right side of the top. ---Bill

Where the soft apholstery of the inner roof of the hardtop stops at the front near the windshield, that's it. Once you've removed it [it's held in place by sturdy clips] you will see the three screws on the left and right sides you can loosen. Once loosened, you can move the recepters for the single screws into alignment with the single screws that hold the hardtop in place. Tighten the single screws on both sides, then tighten the three screws on both sides. Voila', the hardtop is now custom-fitted to your car. ---Phil

installing the hard top, don't forget you can pull the plastic piece off the front of the hardtop to adjust the pins. Pull the plastic piece straight out from both sides, don't hesitate it is not going to break. After removing the plastic piece, use your hard top tool to loosen the 3 screws just enough to allow the front pins to slide freely. Lift the hardtop onto the car letting the back pins drop in freely, then guide the front pins into the holes on the front windshield. The pins will still be loose, so the top front pins should slide in easily. After your top is secure, retighten the 3 screws on each side and push the long plastic piece back into it's slots. Then follow the instructions for hardtop installation now that you have the top sitting securely on the car.
You shouldn't have to do this again in the following years, because the adjustment you just made should be a perfect fit.  ---Julie

If you are having trouble getting the screws at the front of the top to start then you might need to make an adjustment.
Remove the plastic header piece from the front of the hardtop, it just pops off. Around the screws is a plate with 3 screws that can be loosen with the hard top wrench. Slightly loosen the 3 screw on each side. Place the top on the car and put the rear levels in the middle position. Start the screws on both sides in the front. Once the front is tight move the rear levels to the locked position. Tighten the front screws one more time. Then tighten the 3 screw holding the “screw bracket” to the top on each side. Pop the header panel back on. 
Your top is now calibrated to your specific car and you will enjoy the ease of installation from now on. --- Bill

I adjusted mine with the rear pins in the "neutral" position. I loosened the 3 screws on each side, and then tighten the screws that attach the top to the windshield frame. Once tight I locked the rear levers and then tighten the 3 adjustments screws. Made it very easy the next time I installed the top. Pop the header back in place. ---Bill

 trouble after adjustment: 

Give this a try - it might be the ticket. With the top on the car, rear levers in lock position and front screws tight, back off the screws that go into to the top a few turns, maybe 3 or 4. Loosen the 3 adjuster screws on each side. If there is any bind the plates will move slightly even if it is a tiny fraction. Now snug, not tight, up the screws that hold the top to the windshield frame. Tighten the adjusting screws and then tighten the top screws. 
If the female receiving plate is aligned to your specific car, the male screws should, and I repeat should, go right up into the receptacle without doing anything other than to start turning the screws. 
I have only adjusted 2 tops but the results were the same on both and that was / is easy installation. ---Bill

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• "A # 12 Snap On nut driver shortened about an inch will get the hard to reach nut. Snap On is the only one I found that was hollow & would slide over the 4" stud." quote from TBN member
• Other tools may be found that will work.