My house was built in 1909, and has the vast majority of delightful and quirky details that were originally installed. Like the barely cemented-over cistern in the basement, and the lighted push-button switch in the kitchen that turns on the indicator light but doesn't seem to do anything else, and all of the original door knobs, rattling on their little square spindles.
It's not a huge thing, having rattly door knobs, but when you're trying to make your way to the bathroom quietly in the middle of the night it's nicer if they're quiet. Tightening them doesn't really help, because the spindles are just a bit too long, and the square holes on the knobs are worn just a bit, and that's what makes them feel loose, not loose screws.
I fixed them with 2 changes, taking up some slack in both areas. First, I bought some nylon washers with a 3/8" inner diameter and used those behind the knobs. They're about 1/8" thick, and fit within the escutcheon plate, so they're hidden when installed but take up slack from the slightly too-long spindle (or the slightly shrunken 100-year-old maple door). They're a snug fit on the spindle, but not stressed enough to worry about them breaking.
The second fix was for the knob itself. It fits fairly loosely on the square spindle, so i wrapped the end with a few layers of PTFE plumbing tape. It's not tight, but takes up enough space to make it feel better. Between the 2 changes and some fresh lube in the lock mechanism, the doors feel much smoother and tighter, for about 10 minutes work per door.
this is fun, thanks, paul!