Repairing vynil trim
Discolored or broken vinyl trim parts (even if some morsels are missing between the broken parts) can be perfectly repaired using Araldite (or similar) two component epoxy adhesive resins (choose the fast-setting version). The customary plastic packaging used in great volumes today (with paper background and the product shrink wrapped) can be used in the process. Cut out the bigger flat parts of such plastic wrappers. Araldite does not glue to them: even if it seems that it does, it can be easily snapped off once the resin is completely hardened. It is vital to wait until the complete hardening patiently because trying to remove the plastic from the resin before that will ruin your attempts at a clear and nice-looking surface. If in doubt, try first with a small piece of plastic if Araldite sets hard onto it or not. Common adhesive tapes like Scotch Magic Tape (especially the non-permanent version) can also be used as they can be peeled off the fully hardened epoxy resin. As a third alternative, you can use the non-sticky back paper used as the carrier of self-adhevise labels.
Remove the vinyl panel in question. Clean the area to be repaired thoroughly to remove any dirt, oily residue or the remnants of oily trim cleaning products. Cover the hole, crack, broken part of whatever you want to repair on the right side of the panel with adhesive tape (if smaller) or an adequately shaped part of the plastic wrapper mentioned (if the damaged area is bigger). In the second case, use adhesive tape to secure it in its place (Scotch Magic Tape is the best kind to use because it doesn't leave glue residues).
Mix the two components (resin and hardener) of the epoxy adhesive according to the instructions on the packaging. Observe the setting time specified and don't mix more than you can use during this period of time.
Using a small plastic spatula (it usually comes with the epoxy resin), fill the resin into the hole, crack or missing part from the wrong side of the panel. Unless you have to preserve the thickness of the vinyl panel (check beforehand to see if there is room behind the panel), add glue not only to the exact location of the spot to be repaired but a few centimeters around it. Fill it up so that the glue layer is 3-4 millimeters proud of the surface of the panel.
Cover the glue (and the repaired spot beneath it) with a larger piece of wrapper plastic, flat or warped, cut into the form the panel shape requires. Push it down so that the resin beneath it will distribute evenly, filling every hole and crack, forming a flat layer over the panel wrong side surface. Fix the covering plastic in this position with adhesive tape or small clamps. Let the resin harden fully (24 hours in general) then snap off the cover with your nail or a small screwdriver. Remove the adhesive tape or other covering plastic on the right side, too. Curved panels (for instance, A or C pillar interior trim panels) might require more than one session to form the whole surface. If you were careful, the right side is perfectly level with the panel and the wrong side has a very neatly looking, strong epoxy layer, glueing and fortifying the repair.
If the crack is larger or the panel in question must withstand physical stress (like a spoiler or bumper), use a fiberglass reinforcement sheet on the wrong side. Kits with such sheets and the necessary epoxy resin glue are available from Loctite and other manufacturers, generally under the name of Bumper repair kit.
Buy a can of acrylic paint spray (Holts, Multona, Dupli-Color, Sikkens or other makes) matching the color of the vinyl panel. To make the epoxy resin on the right side of the panel absolutely invisible, don't spray the paint onto the panel directly but onto a lint-free cloth instead and use this as a stamper to stamp the paint onto the surface. You can use the same stamping method to repaint parts which are discolored (for instance the top of the dashboard just behind the windshield in cars trimmed in light grey, which is often damaged by direct sunlight). I've already used this method for much more ambitious modifications than simply to combat some discolorations: also to completely change a beige colored trim part into a black one with stunning results.
Acrylic paints dry very quickly. The small amount you stamp on with a cloth becomes dry in one minute or so. They also change their color shade slightly during this time. So, there is no hurry: proceed in small steps. You can always add another thin layer if required but you can hardly remove a thick layer without leaving ugly traces.