I don't know if the wiring is bad it does look like it though ,as your pictures show a lot of blobby solder and long bared wires at the end of the insulation. From what you say some of the wires may not be connecting properly to the pots or other earths - before you go ripping it apart (as you probably know)try very gently moving the wires with the guitar plugged in to see if it makes any difference to hiss pops and crackles.

re: "But as you said, they messed around a lot with their serials and mixed them up without real defined patterns. Or maybe I just don't get it. " yes I don't really understand their numbering system either, I did look it up on the intertent yesterday and it seems that the acid was better in the 60s. :(.

To let you know the score i am "teaching myself" the tech stuff, I've got several cheap fender copies and one Les Paul copy. I have rewired and rebuilt a few fender copies over the last 18 months,(yes i should have learned the thoery by now but haven't :() have not done a LP/Gibson type as mine is a bit too nice to P_iss about with,therefore i can recognise slightly bad wiring, but not give you direct info on SG/LP types ,but those yellow "jumpers" on the back of the pots look dodgy.

I beleive that http://www.guitarnuts.com has an LP diagram on their wiring menu - this should be the same as a SG, it's just got the switch in a different place, hang on i just found it it's here ;

http://www.guitarnuts.com/wiring/stockgibson.html

there aint any jumpers on this thing, a possible suggestion :if you can/know a friend who can solder try taking one end of the yellow wire off the back of a pot.