The "cylindrical object" should be secured to the cable, with solder. That's what allows the cable to move the window. Also, the bracket which attaches to the glass itself should be rigidly secured to the glass, and not waggle from side to side. otherwise it will interfere with the bar from the inner door handle to the outer latch mechanism. Ideally, the thing to do is rebuild the inner guts of the door, as half measures will only cost you more in time and frustration. Take it all out, clean it up, repair or replace what needs it, lube everything, and put it all back together. I know that sounds like overkill, but after 45+ years of rattling, slamming and other abuse some serious attention is usually called for. Might also be a good time to replace the fuzzy window channels.
For the immediate problem. I would take out the whole cable, and find the spot where the cylinder was originally secured, then have it properly resoldered. A lot of people try to wire up, or attach some kind of cable stops, but those seldom last for long. Pay attention to which way was up, and down on the cable, as they aren't symetrical. Wash the chain and cable in solvent, lube the whole thing with white grease, and reinstall. But, if the bracket, or lifter part of the window is loose, it's going to continue to foul and jam up.
So, "a stitch in time saves nine,..."