Engaging the rear brake results in a burning smell and significant brake wear, so bad that within just a hundred miles or so I caused significant loss of material on a brand new pad set. Looking at the brakes after use, I find flakes of brake pad rubber stuck to/falling off of what remains, and the brake has considerably eroded.
The rim is steel. It has a gash/scratch in it that is rough. The rim also has a small dent. Interesting is that both rim pads wore down extremely quickly despite the gash/dent being only on one side of the rim. I don't think the brake is rubbing while riding, because I don't feel excess resistance, and I don't smell the burning when normally riding, only under "heavy" braking (going down a hill for a block or so). However, I did notice that one brake lever can occasionally be slow to retract; but again, extreme wear is on both pads.
I took the wheel into a shop without mentioning this issue, just asking the mechanic if he thought it was safe to ride; he said it would be fine.