I've used that white foamy window cleaner(with amonia added) and xxx steel wool or finer.The amonia helps sluff off the oxidized plastic/fine scratches and the cleaner lubricates and cleans. Only polish back and forth( the longest way) in parallel lines-NO around and around.Don't hang in one spot too long, keep moving evenly over the surface in multiple passes. You won't get it all on the first rub. Don't press down real hard , just "firm".After that, I ragged in silicone spray. It took 3 repeats until I was happy (mines 91 though). Now I use Mothers brand Back IN Black. My Blue bike gleams in the sun. I've not found anything better, but i'd like to hear some ideas too.
The finer the steel wool the shinier your bike will be but it will take more rubbing and elbow grease. If your bikes not bad ,start there or if it's beat bad start with xxx and go one step finer if you can find it. It doesn' t remove the bendy white marks, but helps out. might work good if a guy heats white marks out some then polishes.
If you want something you can quickly get it shined up i would buy a pack of tire wet wipes. They make it look brand new the only drawback is that its not permanant, but if you need it to look good very quickly i found that these work and you can even tell that its on there if you do it right.
Use a really fluffy buffing wheel and some of that white liquidy compound that automotive manufacturers use on the detail process of plastic parts, that stuff will renew CD scratches even. If there are slightly deeper scratches than sand it with 1500 grit sandpaper first on a DA. When done it will look like a brand new car's painted plastics.