Right on! Very cool find, I'm jeasous!! I'd love to find a Burgertime I'd figure out a way to stuff it in my kitchen with the other 2!
You need to adjust the "horizontal width coil" which actually going to adjust your vertical since the monitor is tipped up on end. Buy the Bob Roberts plastic adjustment tool kit. The hor. width coil has copper windings going around it with a hex or slot baby adjustment recessed down in the middle. Don't use a metal allen wrench, it will break it. Only takes a little turn, don't over turn it!! It sounds like you might want to do a cap kit on it just because of the "jittery" that you were mentioning... And on the monitor crooked you'll want to loosen the screws that are on the white collar near the neckboard and carefully rotate the neck board the direction you need it to go. Its a little firm at first, be gentle, but make sure you got the screws loose or you could break the neck of the tube!
On your sound I'd recommend reflowing the solder joints on any header pins or interconnects, anything to do with the sound. Check the connections and make sure nothing is corroded.
On the graphics glitches check your voltages at the board. Your 5v should be no higher than 5.10 and no lower than 5.05 in most cases. Also singly removed each socketed chip and clean the legs up nicely, reseat them carefully, do ALL the chips on the board that can be removed. Make sure to get them in straight and all the legs lined up before you press the chip down firm. They also make a chip removal tool and you want to pull up as straight as possible and carefully when removing. Also clean the edge connector on the pcb, they like to burn on the ground side!