do you plan on repainting the frame?
There are two kinds of people in the world, "Those who help themselves to people, and those who help people!"
have it bead blasted. Then mask off all the holes carefully - put set screws in any threaded ones, a scrap BB in the bottom and old fork cut off in the headset; then have it powder coated.
Nigel
Specialised Globe Vienna 4 bling bling
have some fun with elbow grease, look at this tread in "show off your bike" forum
There are two kinds of people in the world, "Those who help themselves to people, and those who help people!"
Are those scratches or just some kind of funky dirt? If that's dirt, try some 409 and some nylon scrubs (the kind you use on Teflon cookware). If the surface gets a bit dull after using the scrubs, you can use any good quality car wax to shine it back up.
HCFR Cycling Team
Ride Safe...Ride Hard...Ride Daily
Ok, you'll laugh, but on an old bike I start with household cleaners, a sponge like you use for dishes (not the green abrasive side!) & paper towels to quick dry & check progress. First I try Windex, then 409, then simple green. If the gook looks like glue that some idiot got on it I'll try some glue remover, mineral spirits & a quick wipe with lacquer thinner. If that doesn't work I use a damp white athletic sock & Amaz Clean & Green. It's for removing water stains from shower stalls. I have taken old thrashed looking wheels with rusty hubs & made them look brand new. It's kind of like rubbing compound. Put your hand in the damp sock & use your finger tip to work about a 3/4" area, be careful, don't overdo it, check your progress frequently.
By the way, some blue bar tape would look great on that bike. Nice ride.
You could try some T-cut or car paint restorer, this is mildly abrasive and can be used to buff out small scratches or stains on the top layer of paint. Go easy though, you don't want to wear right through the top coat to the undercoat or the bare frame and take care on the decals. You can also use metal polish, something like Brasso which is also mildly abrasive, with similar results.
After you've polished, use a car wax, this will seal and protect the paintwork and help prevent dirt sticking to it.
However, those marks look like they may have actually stained the paintwork and not just be sitting on the top of it, so they may be impossible to polish off.