My 1980 300SD with 114k miles is having some VERY random rough idle issues.
What might be causing this?

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1973 280 - Sold
1980 300SD - Sold
1982 240D - Stolen
1988 300E - Sold
1989 260E - Sold
1989 560SEL
1994 E420 - Sold
1997 E420
2005 CL500

Ideas: Filters, dirty/faulty injectors, rack damper, valve adjustment, motor mounts/shocks, trans. mounts shocks, fuel quality. If you search on each of these, you'll find a bunch of activities you can do to isolate each possiblity. Good luck.

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1998 E300D, 287k, barely broken in.

Since it is random I suspect perhaps air is getting in your system. Does it seem to happen more when your tank is lower? The second thought is if the valve clearances have never been checked for a long time perhaps one is periodically letting a cylinder drop out. It would of course have virtually no clearance when and if you checkedthem.