So I messed around with some paint repair tonight. If your bike is painted black or white and has dings, I would recommend Rustoleum appliance touch-up paint. Cheap and easy. It comes in a little bottle with a brush in the lid. Enough to do a bike and perhaps your washing machine too. Dries in 10 minutes.
I next tried the Turtle stuff. A ketchup packet is about the amount that you need to do a bike - the container they sell you would last 10 lifetimes. Very tame. Didn't turn my cloth any color at all. Totally ineffective against faded paint next to stickers as reported. It does help get off road tar or adhesive or whatever might be on the bike. Highly effective on faded black parts - shocks, cranks, brakes, etc. Perhaps it works for getting swirl marks off of cars, but not particularly useful on a bicycle, except the black parts.
Then I went to wet sanding 800 grit on the white bike with all the touch up paint. This removed paint and the paper turned white repeatedly. Very good at removing stubborn dirty spots. Effective at smoothing over touched up and repainted sections that were obviously rough. Probably too course for most bikes, but perfect for my very beat up bike.